- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 750147, 8 pages
A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations
1Department of Maths and Statistics, Curtin University, Perth, WA 6845, Australia
2School of Statistics & Maths, Zhongnan University of Economics and Law, Wuhan 430073, China
3Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
Received 1 December 2012; Revised 13 March 2013; Accepted 14 March 2013
Academic Editor: Xinguang Zhang
Copyright © 2013 Yanli Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- P. Hu and C. Huang, “Stability of stochastic -methods for stochastic delay integro-differential equations,” International Journal of Computer Mathematics, vol. 88, no. 7, pp. 1417–1429, 2011.
- J. Tan and H. Wang, “Mean-square stability of the Euler-Maruyama method for stochastic differential delay equations with jumps,” International Journal of Computer Mathematics, vol. 88, no. 2, pp. 421–429, 2011.
- N. Jacob, Y. Wang, and C. Yuan, “Numerical solutions of stochastic differential delay equations with jumps,” Stochastic Analysis and Applications, vol. 27, no. 4, pp. 825–853, 2009.
- H. Zhang, S. Gan, and L. Hu, “The split-step backward Euler method for linear stochastic delay differential equations,” Journal of Computational and Applied Mathematics, vol. 225, no. 2, pp. 558–568, 2009.
- W. Wang and Y. Chen, “Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations,” Applied Numerical Mathematics, vol. 61, no. 5, pp. 696–701, 2011.
- V. Kolmanovskii and A. Myshkis, Applied Theory of Fundamental Differential Equations, Kluwer, New York, NY, USA, 1992.
- S. E. A. Mohammed, Stochastic Functional Differential Equations, vol. 99 of Research Notes in Mathematics, Pitman, Boston, Mass, USA, 1984.
- S. E. A. Mohammed, “Lyapunov exponents and stochastic flows of linear and affine hereditary systems,” in Diffusion Processesand Related Problems in Analysis, Volume II, vol. 27 of Progress in Probability, pp. 141–169, Birkhäuser, Boston, Mass, USA, 1992.
- X. Mao, Exponential Stability of Stochastic Differential Equations, vol. 182, Marcel Dekker, New York, NY, USA, 1994.
- X. Mao, Stochastic Differential Equations and Applications, Horwood, New York, NY, USA, 1997.
- S. E. A. Mohammed and M. K. R. Scheutzow, “Lyapunov exponents and stationary solutions for affine stochastic delay equations,” Stochastics and Stochastics Reports, vol. 29, no. 2, pp. 259–283, 1990.
- A. V. Svishchuk and Y. I. Kazmerchuk, “Stability of stochastic Ito equations delays, with jumps and Markov switchings, and their application in finance,” Theory of Probability and Mathematical Statistics, no. 64, pp. 141–151, 2002.
- J. Luo, “Comparison principle and stability of Ito stochastic differential delay equations with Poisson jump and Markovian switching,” Nonlinear Analysis: Theory, Methods and Applications A, vol. 64, no. 2, pp. 253–262, 2006.
- R. Li and Z. Chang, “Convergence of numerical solution to stochastic delay differential equation with Poisson jump and Markovian switching,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 451–463, 2007.
- P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, vol. 23 of Applied Mathematics, 3rd corrected printing, Springer, Berlin, Germany, 1999.
- U. Küchler and E. Platen, “Strong discrete time approximation of stochastic differential equations with time delay,” Mathematics and Computers in Simulation, vol. 54, no. 1–3, pp. 189–205, 2000.
- C. T. H. Baker and E. Buckwar, “Introduction to the numerical analysis of stochastic delay differential equations,” Numberical Analysis Report 345, University of Manchester, Department of Mathematics, Manchester, UK, 1999.
- H. Gilsing, “On the stability of the Euler scheme for an affine stochastic differential equations with time delay,” Diskussion Paper 20, SFB 373, Humboldt University, Berlin, Germany, 2001.
- C. Tudor and M. Tudor, “On approximation of solutions for stochastic delay equations,” Studii şi Cercetări Matematice, vol. 39, no. 3, pp. 265–274, 1987.
- C. Tudor, “Approximation of delay stochastic equations with constant retardation by usual Itô equations,” Revue Roumaine de Mathématiques Pures et Appliquées, vol. 34, no. 1, pp. 55–64, 1989.
- E. Platen and N. Bruti-Liberati, Numerical Solution of Stochastic Differential Equations with Jumps in Finance, vol. 64 of Stochastic Modelling and Applied Probability, Springer, Berlin, Germany, 2010.
- R. Mikulevičius and E. Platen, “Time discrete Taylor approximations for Itô processes with jump component,” Mathematische Nachrichten, vol. 138, pp. 93–104, 1988.
- C. L. Evans, An Introduction to Stochastic Differential Equations, Lecture Notes, University of California, Department of Mathematics, Berkeley, Calif, USA, 2006.