\(L^p(p > 2)\)-strong convergence of an averaging principle for two-time-scales jump-diffusion stochastic differential equations
The authors study the \(L^p\) (\(p > 2\))-strong convergence of the averaging principle (see [\textit{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 \textit{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)], \textit{D. Givon} et al. [Commun. Math. Sci. 4, No. 4, 707--729 (2006; Zbl 1115.60036)] or \textit{G. Wainrib} [Electron. Commun. Probab. 18, Paper No. 51, 12 p. (2013; Zbl 1297.70015)].
scientific article; zbMATH DE number 6523030
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