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An averaging principle for stochastic dynamical systems with Lévy noise. (English) Zbl 1236.60060
Taking into consideration that Poisson noise is a special non-Gaussian Lévy noise, the authors study the averaging principle for a class of stochastic differential equations with Poisson noise, (see, e.g., [I. M. Stojanov and D. D. Bainov, Ukr. Math. J. 26(1974), 186–194 (1975; Zbl 0294.60051)]) for stochastic differential equations in \(\mathbb R^d\) with Lévy noise. Solutions to stochastic systems with Lévy noise can be approximated by solutions to averaged stochastic differential equations in the sense of both convergence in mean square and convergence in probability. The convergence order is estimated in terms of noise intensity. Two examples are presented, and a numerical simulation is carried out.

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
Full Text: DOI
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