Weak order in averaging principle for stochastic differential equations with jumps

Bengong Zhang; Hongbo Fu; Jicheng Liu; Li Wan

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Weak order in averaging principle for stochastic differential equations with jumps

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arxiv 1701.07983 v3 pith:RSESUW5A submitted 2017-01-27 math.PR

Bengong Zhang , Hongbo Fu , Li Wan , Jicheng Liu This is my paper

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keywords weakconvergenceaveragingdifferentialorderprincipleratestochastic

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abstract

The present article deals with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equation. Under suitable conditions, the weak error is expanded in powers of timescale parameter. It is proved that the rate of weak convergence to the averaged dynamics is of order $1$. This reveals the rate of weak convergence is essentially twice that of strong convergence.

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