### John Appleby

Prof

### Book

Year | Publication | |
---|---|---|

2010 |
Terry Lynch and John A D Appleby (2010) : LAP LAMBERT Academic Publishing. Large Fluctuations of Stochastic Differential
Equations: Regime Switching and Applications to Simulation and Finance. | |

2010 |
Huizhong Wu and John A. D. Appleby (2010) : LAP Lambert Academic Publishing. Pathwise Large Deviations of Stochastic Differential Equations with Applications to Finance. | |

2010 |
Catherine Swords and John A. D. Appleby (2010) : LAP Lambert Academic Publishing. Stochastic Delay Difference and Differential Equations: Applications to Financial Markets. | |

2007 |
Appleby, J.A.D.; Edelman, D.C.; Miller, J.J.H. (2007) [Link] Numerical methods for finance. | |

2007 |
John H. Miller, David Edelman and John A. D. Appleby (2007) : Chapman & Hall/CRC Press. Numerical Methods in Finance. |

### Peer Reviewed Journal

Year | Publication | |
---|---|---|

2018 |
Appleby, J.A.D.; Patterson, D.D. (2018) 'Blow–up and superexponential growth in superlinear volterra equations'. Discrete and Continuous Dynamical Systems- Series A, 38 . [Link] [DOI] | |

2018 |
Appleby, John A. D.; Patterson, Denis D. (2018) 'GROWTH RATES OF SUBLINEAR FUNCTIONAL AND VOLTERRA DIFFERENTIAL EQUATIONS'. SIAM Journal on Mathematical Analysis, 50 (2). [DOI] | |

2017 |
John A. D. Appleby (2017) 'Exact and memory-dependent decay rates to the non-hyperbolic equilibrium of differential equations with unbounded and maximum functional'. Electronic Journal of Qualitative Theory of Differential Equations, . | |

2017 |
Appleby, John A. D.; Patterson, Denis D. (2017) 'MEMORY DEPENDENT GROWTH IN SUBLINEAR VOLTERRA DIFFERENTIAL EQUATIONS'. Journal of Integral Equations and Applications, 29 (4). [DOI] | |

2017 |
Appleby, J.A.D.; Patterson, D.D. (2017) 'Hartman-Wintner growth results for sublinear functional differential equations'. Electronic Journal of Differential Equations, 2017 . [Link] | |

2017 |
Appleby, John A. D.; Patterson, Denis D. (2017) 'Large fluctuations and growth rates of linear Volterra summation equations'. Journal of Difference Equations and Applications, 23 (6). [DOI] | |

2017 |
John A. D. Appleby, Denis D. Patterson (2017) 'Memory dependent growth in sublinear Volterra equations'. Journal of Integral Equations and Applications, . | |

2017 |
Appleby, J.A.D.; Patterson, D.D. (2017) 'Growth rates of solutions of superlinear ordinary differential equations'. Applied Mathematics Letters, 71 . [Link] [DOI] | |

2016 |
Appleby, John A. D.; Patterson, Denis D. (2016) 'On the admissibility of unboundedness properties of forced deterministic and stochastic sublinear Volterra summation equations'. Electronic Journal of Qualitative Theory of Differential Equations, (63). [DOI] | |

2015 |
Appleby, J; Patterson, D (2015) 'Subexponential growth rates in functional differential equations'. Discrete and Continuous Dynamical Systems - Series S, Volume 2015 :56-65. [DOI] | |

2014 |
Rodkina, Alexandra; Dokuchaev, Nikolai; Appleby, John (2014) 'On limit periodicity of discrete time stochastic processes'. Stochastics and Dynamics, 14 (4). [DOI] | |

2013 |
Appleby, John A. D.; Riedle, Markus; Swords, Catherine (2013) 'Bubbles and crashes in a Black-Scholes model with delay'. Finance and Stochastics, 17 (1). [DOI] | |

2012 |
Appleby, John A. D.; Daniels, John A. (2012) 'Long run behaviour of the autocovariance function of ARCH(∞) models'. Journal of Mathematical Analysis and Applications, 392 (2). [DOI] | |

2012 |
Appleby, John A. D.; Daniels, John A. (2012) 'Necessary and sufficient conditions for periodic decaying resolvents in linear discrete convolution Volterra equations and applications to ARCH(∞) processes'. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 64 (7). [DOI] | |

2011 |
John A. D. Appleby and John A. Daniels (2011) 'Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles'. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, SERIES A, Supplement :91-101. | |

2011 |
Appleby, J.A.D.; Rodkina, A.; Schurz, H. (2011) 'On an exponential martingale approach to almost sure stability of itô sdes in R. ^{1}'Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 18 . [Link] | |

2011 |
John A. D. Appleby, Jian Cheng and Alexandra Rodkina
(2011) 'Characterisation of the asymptotic behaviour of scalar linear differential equations with respect to a fading stochastic perturbation'. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, SERIES A, Supplement :79-90. | |

2011 |
John A. D. Appleby and Katja Krol (2011) 'Long memory in a linear stochastic Volterra equation'. Journal of Mathematical Analysis and Applications, 380 :814-830. | |

2011 |
John A. D. Appleby, David W. Reynolds and Istvan Gyori (2011) 'History--dependent decay rates for a logistic
equation with infinite delay'. Proceedings of Royal Society Edinburgh, Section A, 141 :23-44. | |

2011 |
Appleby, John A. D.; Krol, Katja (2011) 'Long memory in a linear stochastic Volterra differential equation'. Journal of Mathematical Analysis and Applications, 380 (2). [DOI] | |

2011 |
Appleby, J.A.D.; Daniels, J.A. (2011) 'Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles'. Discrete and Continuous Dynamical Systems- Series A, . [Link] | |

2011 |
Appleby, J.A.D.; Cheng, J.; Rodkina, A. (2011) 'Characterisation of the asymptotic behaviour of scalar linear differential equations with respect to a fading stochastic perturbation'. Discrete and Continuous Dynamical Systems- Series A, . [Link] | |

2011 |
John A. D. Appleby, Alexandra Rodkina, and Henri Schurz (2011) 'On an exponential martingale approach to almost sure stability of Itô SDEs in R^1'. DYNAMICS OF CONTINUOUS, DISCRETE & IMPULSIVE SYSTEMS. SERIES A. MATH ANAL, 18 :471-484. | |

2010 |
Appleby, J.A.D. (2010) 'On the positivity and zero crossings of solutions of stochastic volterra integrodifferential equations'. International Journal of Differential Equations, 2010 . [Link] [DOI] | |

2010 |
John A. D. Appleby (2010) 'On the Positivity and Zero Crossings of Solutions of Stochastic Volterra Integrodifferential Equations'. Volume 2010 :1-25. | |

2010 |
John A. D. Appleby and Markus Riedle (2010) 'Stochastic Volterra differential equations in weighted
spaces'. Journal of Integral Equations and Applications, 22 :1-17. | |

2010 |
Appleby, John A. D. (2010) 'On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory'. Advances in Difference Equations, . [DOI] | |

2010 |
John A. D. Appleby, Jian Cheng, and Alexandra Rodkina (2010) 'The split-step Euler--Maruyama method preserves asymptotic stability for simulated annealing problems
'. PROCEEDINGS OF DYNAMIC SYSTEMS AND APPLICATIONS, Volume 4 :31-36. | |

2010 |
John A. D. Appleby (2010) 'History--Dependent and Regularly Varying Convergence Rates of Solutions of Infinite Memory Volterra Integrodifferential Equations'. Advances in Difference Equations, Volume 2010 :1-31. | |

2010 |
John A.D. Appleby, Xuerong Mao, Conall Kelly, and Alexandra Rodkina (2010) 'On the local dynamics of polynomial difference equations with fading stochastic perturbations'. DYNAMICS OF CONTINUOUS, DISCRETE & IMPULSIVE SYSTEMS. SERIES A. MATH ANAL, 17 :401-430. | |

2010 |
John A. D. Appleby, Conall Kelly and Alexandra Rodkina (2010) 'On the use of adaptive meshes to counter overshoot in solutions of discretised nonlinear stochastic differential equations'. 5 :129-148. | |

2010 |
Appleby, J.; Kelly, C.; Mao, X.; Rodkina, A. (2010) 'On the local dynamics of polynomial difference equations with fading stochastic perturbations'. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 17 . [Link] | |

2010 |
John A. D. Appleby, Xuerong Mao and Huizhong Wu (2010) 'On the almost sure partial maxima of solutions of
affine stochastic functional differential equations'. 42 :646-678. | |

2010 |
Appleby, J.A.D.; Buckwar, E. (2010) 'A Constructive Comparison Technique for Determining the Asymptotic Behaviour of Linear Functional Differential Equations with Unbounded Delay'. Differential Equations and Dynamical Systems, 18 . [Link] [DOI] | |

2010 |
Appleby, John A. D.; Mao, Xuerong; Wu, Huizhong (2010) 'ON THE ALMOST SURE RUNNING MAXIMA OF SOLUTIONS OF AFFINE STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS'. SIAM Journal on Mathematical Analysis, 42 (2). [DOI] | |

2010 |
John A. D. Appleby and Evelyn Buckwar (2010) 'A constructive comparison technique for determining the asymptotic behaviour of linear functional differential equations with unbounded delay'. 18 :271-301. | |

2010 |
John A. D. Appleby, Malgorzata Guzowska, Alexandra Rodkina, and Conall Kelly (2010) 'Preservation of positivity in the solution of
discretised stochastic differential equation'. Applied Mathematics and Computation, 217 :763-774. | |

2010 |
Appleby, John A. D.; Riedle, Markus (2010) 'STOCHASTIC VOLTERRA EQUATIONS IN WEIGHTED SPACES'. Journal of Integral Equations and Applications, 22 (1). [DOI] | |

2010 |
John A. D. Appleby, Michael J. McCarthy and Alexandra Rodkina (2010) 'Exact growth rates of solutions of delay--dominated differential equations
'. PROCEEDINGS OF DYNAMIC SYSTEMS AND APPLICATIONS, Volume 4 :37-42. | |

2010 |
Appleby, John A. D.; Rodkina, Alexandra; Schurz, Henri (2010) 'Non-positivity and oscillations of solutions of nonlinear stochastic difference equations with state-dependent noise'. Journal of Difference Equations and Applications, 16 (7). [DOI] | |

2009 |
John A. D. Appleby, Alexandra Rodkina and Lih--Ing W. Roeger (2009) 'Stability of a limit cycle for a planar system with stochastic perturbations'. FUNCTIONAL DIFFERENTIAL EQUATIONS, 16 :73-91. | |

2009 |
John A. D. Appleby, Alexandra Rodkina, and Gregory Berkolaiko (2009) 'Nonexponential stability and Decay Rates of Nonlinear
Stochastic Difference Equations with unbounded noises'. STOCHASTICS AND STOCHASTICS REPORTS, 81 :99-127. | |

2009 |
John A. D. Appleby and Alexandra Rodkina (2009) 'Stability of Nonlinear Stochastic Volterra Difference Equations with Respect to a Fading Perturbation'. 4
:165-184. | |

2009 |
Appleby, John A. D.; Berkolaiko, Gregory; Rodkina, Alexandra (2009) 'Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise'. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 81 (2). [DOI] | |

2009 |
John A. D. Appleby and Catherine Swords (2009) 'Asymptotic behaviour of a nonlinear stochastic
difference equation modelling an inefficient financial market'. Adv. Stud. Pure Math. 53 :23-33. | |

2009 |
John A.D. Appleby and Huizhong Wu (2009) 'Solutions of stochastic differential equations obeying
the law of the iterated logarithm with applications to financial markets'. Electronic Journal of Probability, 14 :912-959. | |

2009 |
John A. D. Appleby, Alexandra Rodkina, and Markus Riedle (2009) 'On Asymptotic Stability of linear stochastic Volterra
difference equations with respect to a fading perturbation'. Adv. Stud. Pure Math. 53 :271-282. | |

2009 |
John A. D. Appleby, Conall Kelly, Xuerong Mao, and Alexandra Rodkina (2009) 'Positivity and stabilization for nonlinear stochastic
delay differential equations'. STOCHASTICS AND STOCHASTICS REPORTS, 81 :29-54. | |

2009 |
John A. D. Appleby, Alexandra Rodkina and Henri Schurz (2009) 'On the oscillation of solutions of stochastic difference equations
'. MATEMATICAS: ENSENANZA UNIVERSITARIA, 17 :1-10. | |

2009 |
John A. D. Appleby, Michael J. McCarthy and Alexandra Rodkina (2009) 'Growth rates of delay-differential equations and uniform Euler schemes'. Difference Equations and Applications :117-124. | |

2009 |
John A.D. Appleby, Terry Lynch, Xuerong Mao, and Huizhong Wu (2009) 'The Size of the Largest Fluctuations in a Market Model
with Markovian Switching'. 13 :135-166. | |

2009 |
Appleby, John A. D.; Kelly, Conall; Mao, Xuerong; Rodkina, Alexandra (2009) 'Positivity and stabilisation for nonlinear stochastic delay differential equations'. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 81 (1). [DOI] | |

2009 |
John A. D. Appleby, James Gleeson, and Alexandra Rodkina (2009) 'Stability under fading stochastic perturbations of
globally stable nonlinear differential equations'. 88 :579-603. | |

2008 |
John A. D. Appleby and Huizhong Wu (2008) 'Exponential growth and Gaussian--like fluctuations of
solutions of stochastic differential equations with maximum functionals'. JOURNAL OF PHYSICS : CONFERENCE SERIES (PRINT), 138 :1-25. | |

2008 |
John A. D. Appleby, Xuerong Mao and Alexandra Rodkina (2008) 'Stabilization and destabilization of nonlinear
differential equations by noise'. IEEE Transactions on Automatic Control, 53 :683-691. | |

2008 |
John A.D. Appleby, Alexandra Rodkina, and James
Gleeson (2008) 'Asymptotic constancy and stability in nonautonomous
stochastic differential equations'. 10 :145-160. | |

2008 |
John A. D. Appleby (2008) 'Convergence rates of the solution of a Volterra-type
stochastic differential equations to a non-equilibrium limit'. ELEC JNL QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, Proc. 8th Coll. QTDE :1-30. | |

2008 |
Appleby, J.A.D.; MacKey, D.; Rodkina, A. (2008) 'Almost sure polynomial asymptotic stability of stochastic difference equations'. Journal of Mathematical Sciences, 149 . [Link] [DOI] | |

2008 |
Appleby, J.; Berkolaiko, G.; Rodkina, A. (2008) 'On local stability for a nonlinear difference equation with a non-hyperbolic equilibrium and fading stochastic perturbations'. Journal of Difference Equations and Applications, 14 (9). [DOI] | |

2008 |
John A. D. Appleby, Dana Mackey, and Alexandra Rodkina (2008) 'Almost sure polynomial asymptotic stability of
stochastic difference equations,
Journal of Mathematical Sciences'. 149 :1629-1647. | |

2008 |
John A. D. Appleby, Siobhan Devin, David Reynolds (2008) 'Characterisation of exponential convergence to
non--equilibrium limits for stochastic Volterra equations'. Journal of Applied Mathematics and Stochastic Analysis, Volume 2008 :1-27. | |

2008 |
Appleby, J.A.D.; Devin, S.; Reynolds, D.W. (2008) 'Characterisation of exponential convergence to nonequilibrium limits for stochastic Volterra equations'. Journal of Applied Mathematics and Stochastic Analysis, 2008 . [Link] [DOI] | |

2008 |
John A. D. Appleby, Gregory Berkoliako and Alexandra Rodkina (2008) 'On Local Stability for a Nonlinear Difference Equation
with a Non-Hyperbolic Equilibrium and Fading Stochastic
Perturbations'. Journal of Difference Equations and Applications, 14 :923-951. | |

2008 |
John A. D. Appleby and David Reynolds (2008) 'Decay rates of solutions of linear stochastic Volterra
equations'. Electronic Journal of Probability, 13 :922-943. | |

2008 |
Appleby, J.A.D.; Reynolds, D.W. (2008) 'Decay rates of solutions of linear stochastic volterra equations'. Electronic Journal of Probability, 13 . [Link] | |

2008 |
John A. D. Appleby, Alexandra Rodkina, and Catherine Swords
(2008) 'Fat Tails and Bubbles in a Discrete Time Model of an
Inefficient Financial Market'. PROCEEDINGS OF DYNAMIC SYSTEMS AND APPLICATIONS, 5 :35-45. | |

2007 |
John A. D. Appleby, Siobhan Devin and David W. Reynolds (2007) 'Almost sure convergence of solutions of linear stochastic Volterra equations to nonequilibrium limits'. Journal of Integral Equations and Applications, 19
:405-437. | |

2007 |
John A. D. Appleby, Malgorzata Guzowska, and Alexandra Rodkina (2007) 'On polynomial rate of decay and growth of solution to
nonlinear difference equations'. REVISTA DE MATEMATICA: TEORIA Y APLICACIONES, 14
:33-44. | |

2007 |
Reynolds, D.W.; Appleby, J.A.D.; Gyori, I. (2007) 'On exact rates of growth and decay of solutions of a linear Volterra equation in linear viscoelasticity'. Note di Matematica, 27 . [Link] | |

2007 |
John A. D. Appleby and Alexandra Rodkina (2007) 'On the Oscillation of Solutions of Stochastic Difference Equations with State-Independent Perturbations'. 2 :139-164. | |

2007 |
Appleby, J.A.D.; Devin, S.; Reynolds, D.W. (2007) 'Almost sure convergence of solutions of linear stochastic volterra equations to nonequilibrium limits'. Journal of Integral Equations and Applications, 19 . [Link] [DOI] | |

2007 |
John A. D. Appleby and Conall Kelly (2007) 'Spurious oscillation in an Euler discretisation of linear stochastic differential equations with vanishing delay'. Journal of Computational and Applied Mathematics, 205 :923-935. | |

2006 |
John A. D. Appleby, David W. Reynolds, and Siobhan Devin (2006) 'Mean square convergence of solutions of linear Ito Volterra equations to non-equilibrium limits'. DYNAMICS OF CONTINUOUS, DISCRETE & IMPULSIVE SYSTEMS. SERIES A. MATH ANAL, 13B :515-534. | |

2006 |
John A. D. Appleby, Xuerong Mao, and Alexandra Rodkina (2006) 'On stochastic stabilization of difference equations
'. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, SERIES A, 15 :843-857. | |

2006 |
John A. D. Appleby and Markus Riedle (2006) 'Almost sure asymptotic stability of stochastic Volterra
integro-differential equations with fading perturbations'. STOCHASTIC ANALYSIS AND ITS APPLICATIONS, 24 :813-826. | |

2006 |
John A. D. Appleby, Istvan Gyori, and David W. Reynolds (2006) 'On exact convergence rates of solutions of linear systems of Volterra difference equations'. Journal of Difference Equations and Applications, 12 :1257-1275. | |

2006 |
John A. D. Appleby and Aoife Flynn (2006) 'Stabilization of Volterra equations by noise
'. Journal of Applied Mathematics and Stochastic Analysis, 2006 :1-29. | |

2006 |
John A. D. Appleby, Alexandra Rodkina, and Henri Schurz (2006) 'Pathwise non-exponential decay rates of solutions of
scalar nonlinear stochastic differential equations
'. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, SERIES B, 6 :667-696. | |

2006 |
John A. D. Appleby and Conall Kelly (2006) 'Oscillation of solutions of a nonuniform discretisation of linear stochastic differential equations with vanishing delay'. DYNAMICS OF CONTINUOUS, DISCRETE & IMPULSIVE SYSTEMS. SERIES A. MATH ANAL, 13B :535-550. | |

2006 |
John A. D. Appleby and Conall Kelly (2006) 'Prevention of Explosions in Solutions of Functional
Differential Equations by Noise Perturbation
'. Dynamic Systems and Applications, 15 :227-240. | |

2006 |
John A. D. Appleby, Mauro Fabrizio, Barbara Lazzari and
David W. Reynolds (2006) 'On exponential asympototic stability in linear viscoelasticity'. Mathematical Models and Methods in Applied Sciences, 16 :1677-1694. | |

2005 |
John A.D. Appleby and Evelyn Buckwar (2005) 'Noise induced oscillation in solutions of stochastic delay differential equations
'. Dynamic Systems and Applications, 14 :175-197. | |

2005 |
John A. D. Appleby, Xuerong Mao, and Alexandra Rodkina (2005) 'Pathwise superexponential decay rates of solutions of
autonomous stochastic differential equations'. STOCHASTICS AND STOCHASTICS REPORTS, 77 :241-270. | |

2005 |
John A. D. Appleby, Siobhan Devin and David Reynolds (2005) 'Exponential convergence to a nontrivial limit in linear
Volterra integrodifferential equations
'. ELEC JNL QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2005 :1-16. | |

2005 |
Appleby, J.A.D. (2005) 'Decay and growth rates of solutions of scalar stochastic delay differential equations with unbounded delay and state-dependent noise'. Stochastics and Dynamics, 5 . [Link] [DOI] | |

2005 |
John A. D. Appleby (2005) 'Decay and growth rates of solutions of scalar
stochastic delay differential equations with unbounded delay and state dependent noise'. Stochastics and Dynamics, 5 :133-147. | |

2005 |
John A. D. Appleby and Alexandra Rodkina (2005) 'On the asymptotic stability of polynomial stochastic
delay differential equations
'. FUNCTIONAL DIFFERENTIAL EQUATIONS, 12 :35-66. | |

2005 |
John A. D. Appleby and Alexandra Rodkina (2005) 'Rates of decay and growth of solutions to linear
stochastic differential equations with state-independent perturbations'. STOCHASTICS AND STOCHASTICS REPORTS, 77 :271-295. | |

2005 |
John A. D. Appleby (2005) 'Exponential asymptotic stability of nonlinear
Ito-Volterra equations with damped stochastic perturbations'. FUNCTIONAL DIFFERENTIAL EQUATIONS, 12 :7-34. | |

2005 |
John A. D. Appleby and Xuerong Mao (2005) 'Stochastic Stabilisation of Functional Differential
Equations'. Systems and Control Letters, 54 :1069-1081. | |

2004 |
John A. D. Appleby and Conall Kelly (2004) 'Oscillation and non-oscillation in solutions of
nonlinear stochastic delay differential equations'. Electronic Communications in Probability, 9 :106-118. | |

2004 |
John A. D. Appleby and David W. Reynolds (2004) 'On necessary and sufficient conditions for exponential
stability in linear Volterra integro--differential equations
'. Journal of Integral Equations and Applications, 16 :221-240. | |

2004 |
John A. D. Appleby, Istvan Gyori, and David W. Reynolds,
(2004) 'Subexponential solutions of linear scalar integrodifferential equations with a delay
'. FUNCTIONAL DIFFERENTIAL EQUATIONS, 11
:11-18. | |

2004 |
John A. D. Appleby and David W. Reynolds (2004) 'Subexponential solutions of linear integrodifferential
equations'. PROCEEDINGS OF DYNAMIC SYSTEMS AND APPLICATIONS, 4 :488-494. | |

2004 |
John A. D. Appleby and Dana Mackey (2004) 'Polynomial asymptotic stability of damped stochastic
differential equations'. ELEC JNL QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, Proc. 7th Coll. QTDE :1-33. | |

2004 |
John A.D. Appleby and Conall Kelly (2004) 'Asymptotic and oscillatory properties of linear
stochastic delay differential equations with
vanishing delay'. FUNCTIONAL DIFFERENTIAL EQUATIONS, 11 :235-265. | |

2004 |
John A. D. Appleby (2004) 'Subexponential solutions of scalar linear Ito-Volterra equations with damped stochastic perturbations
'. FUNCTIONAL DIFFERENTIAL EQUATIONS, 11
:5-10. | |

2004 |
John A. D. Appleby (2004) 'Almost sure subexponential decay rates of scalar Ito-Volterra equations
'. ELEC JNL QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, Proc. 7th Coll. QTDE :1-32. | |

2004 |
John A. D. Appleby and David W. Reynolds (2004) 'On the nonexponential decay to equilibrium of solutions
of nonlinear scalar Volterra integro-differential equations
'. ELEC JNL QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, Proc. 7th. Coll. QTDE :1-14. | |

2003 |
John A. D. Appleby and David W. Reynolds (2003) 'Non-exponential stability of scalar stochastic Volterra equations
'. Statistics and Probability Letters, 62 :335-343. | |

2003 |
John A. D. Appleby (2003) 'p-th-mean integrability and almost sure asymptotic
stability of Ito-Volterra equations.
'. Journal of Integral Equations and Applications, 15 :321-341. | |

2003 |
Appleby, J.A.D. (2003) 'Exponential asymptotic stability of linear itô-volterra equations with damped stochastic perturbations'. Electronic Journal of Probability, 8 . [Link] [DOI] | |

2003 |
Appleby, J.A.D. (2003) 'Pth mean integrability and almost sure asymptotic stability of solutions of itô-volterra equations'. Journal of Integral Equations and Applications, 15 . [Link] [DOI] | |

2003 |
John A. D. Appleby and Alan Freeman (2003) 'Exponential asymptotic stability of linear Ito-Volterra equations with damped stochastic perturbations
'. Electronic Journal of Probability, 8
:1-22. | |

2003 |
John A. D. Appleby and David W. Reynolds (2003) 'Corrigendum Subexponential solutions of linear
Volterra integro-differential equations and transient renewal equations'. Proceedings of Royal Society Edinburgh, Section A, 133 :1421-1421. | |

2002 |
John A. D. Appleby and David W. Reynolds (2002) 'Subexponential solutions of linear integro-differential equations and transient renewal equations
'. Proceedings of Royal Society Edinburgh, Section A, 132 :521-543. | |

2002 |
John A. D. Appleby and David W. Reynolds (2002) 'On the Non-Exponential Convergence of Asymptotically Stable
Solutions of Linear Scalar Volterra Integro-Differential Equations
'. Journal of Integral Equations and Applications, 14 :109-118. | |

2002 |
John A. D. Appleby (2002) 'Almost sure stability of linear Ito-Volterra equations with damped stochastic perturbations
'. Electronic Communications in Probability, 7 :223-234. | |

2000 |
John A. D. Appleby (2000) 'Heterogeneity and seasonaility in financial markerts
'. International Journal of Theoretical and Applied Finance, 3 :491-492. | |

2000 |
John A.D. Appleby (2000) 'Exponential asymptotic stability for linear volterra equations'. Mathematical Proceedings of the Royal Irish Academy, :1-7. | |

2012 |
Appleby, John A. D.; McCarthy, Michael J. (2012) 'Preservation of the growth rates of delay differential equations by Euler schemes with non-uniform step sizes'. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 64 (7). [DOI] |

### Conference Publication

Year | Publication | |
---|---|---|

2011 |
Appleby, J.A.D.; Gyori, I.; Reynolds, D.W. (2011) Proceedings of the Royal Society of Edinburgh Section A: Mathematics [Link] [DOI] History-dependent decay rates for a logistic equation with infinite delay | |

2014 |
Appleby, J.A.D.; Patterson, D.D. (2014) Springer Proceedings in Mathematics and Statistics [Link] [DOI] On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity | |

2012 |
Appleby, J.A.D.; Daniels, J.A. (2012) [Link] [DOI] Necessary and sufficient conditions for periodic decaying resolvents in linear discrete convolution Volterra equations and applications to ARCH (∞) processes | |

2009 |
Appleby, J.A.D.; Lynch, T.; Mao, X.; Wu, H. (2009) [Link] The size of the largest fluctuations in a market model with markovian switching | |

2007 |
Appleby, J.; Berkolaiko, G.; Rodkina, A. (2007) DIFFERENCE EQUATIONS, SPECIAL FUNCTIONS AND ORTHOGONAL POLYNOMIALS ON THE ASYMPTOTIC BEHAVIOR OF THE MOMENTS OF SOLUTIONS OF STOCHASTIC DIFFERENCE EQUATIONS | |

2003 |
Appleby, J.A.D.; Reynolds, D.W. (2003) [Link] Subexponential solutions of linear integro- differential equations |

### Conference Contribution

### Erratum

Year | Publication | |
---|---|---|

2003 |
Appleby J.; Reynolds, D (2003) ERRAT [DOI] Corrigendum: Subexponential solutions of linear integro-differential equations and transient renewal equations''. |

### Other Publication

Year | Publication | |
---|---|---|

2007 |
Appleby, J.A.D.; Edelman, D.C.; Miller, J.J.H. (2007) [Link] Preface. | |

2007 |
Appleby, J.A.D.; Gyori, I.; Reynolds, D.W. (2007) [Link] [DOI] Erratum: On exact convergence rates for solutions of linear systems of Volterra difference equations (Journal of Difference Equations and Applications (2006) 12, 12). | |

2003 |
Appleby, J.A.D.; Reynolds, D.W. (2003) [Link] Erratum: Subexponential solutions of linear integro-differential equations and transient renewal equations (Proceedings of the Royal Society of Edinburgh (2002) 132A (521-543)). |

Certain data included herein are derived from the © Web of Science (2024) of Clarivate. All rights reserved.

### Research Interests

Deterministic and stochastic functional differential equations,
Stochastic Analysis, Mathematical Finance.