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Zbl 1120.65003
Li, Ronghua; Chang, Zhaoguang
Convergence of numerical solution to stochastic delay differential equation with Poisson jump and Markovian switching. (English)
[J] Appl. Math. Comput. 184, No. 2, 451-463 (2007). ISSN 0096-3003

Authors' summary: The main purpose of this paper is to study the convergence of numerical solutions to a class of stochastic delay differential equations with Poisson jump and Markovian switching. A numerical approximation scheme is proposed to approximate the solution to stochastic delay differential equations with Poisson jump and Markovian switching. It is proved that the Euler approximation solution converge to the analytic solution in probability under weaker conditions. Some known results are generalized and improved. An example is provided to illustrate our theory.
[Grigori N. Milstein (Ekaterinburg)]

MSC 2000:: *65C30 Stochastic differential and integral equations
34K50 Stochastic delay equations
60H10 Stochastic ordinary differential equations
65L20 Stability of numerical methods for ODE

Keywords: stochastic delay differential equation; Poisson jump; Markovian switching; Euler approximation; numerical examples; convergence

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