\(L^p(p > 2)\)-strong convergence of an averaging principle for two-time-scales jump-diffusion stochastic differential equations. (English) Zbl 1384.34070

Xu, Jie; Miao, Yu

Nonlinear Anal., Hybrid Syst. 18, 33-47 (2015).

The authors study the \(L^p\) (\(p > 2\))-strong convergence of the averaging principle (see [R. Z. Has’minskij, Kybernetika 4, 260–279 (1968; Zbl 0231.60045)]) for a class of stochastic differential equations.
In fact, under suitable conditions, it is shown that the slow component \(L^p\) \((p>2)\)-strongly converges to the solution of the corresponding averaging equation (Theorem 4.1).
Their result extend some interesting results given by D. Liu [Commun. Math. Sci. 8, No. 4, 999–1020 (2010; Zbl 1208.60057); Front. Math. China 7, No. 2, 305–320 (2012; Zbl 1255.60098)], D. Givon et al. [Commun. Math. Sci. 4, No. 4, 707–729 (2006; Zbl 1115.60036)] or G. Wainrib [Electron. Commun. Probab. 18, Paper No. 51, 12 p. (2013; Zbl 1297.70015)].

Reviewer: Romeo Negrea (Timişoara)

MSC:

34F05	Ordinary differential equations and systems with randomness
34C29	Averaging method for ordinary differential equations
34E15	Singular perturbations for ordinary differential equations
60J75	Jump processes (MSC2010)
60H20	Stochastic integral equations

Keywords:

stochastic differential equations; stochastic averaging principle; \(L^p\)–strong convergence

Citations:

Zbl 0231.60045; Zbl 1208.60057; Zbl 1255.60098; Zbl 1115.60036; Zbl 1297.70015

References:

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