Limit theorems with asymptotic expansions for stochastic processes

Xiangfeng Yang

Stochastic Processes and their Applications, 2013, vol. 123, issue 1, 131-155

Abstract: In this paper, we consider some families of one-dimensional locally infinitely divisible Markov processes {ηtϵ}0≤t≤T with frequent small jumps. For a smooth functional F(x[0,T]) on space D[0,T], the following asymptotic expansions for expectations are proved: as ϵ→0,EϵF(ηϵ[0,T])=EF(η0[0,T])+∑i=1sϵi/2EAiF(η0[0,T])+o(ϵs/2) for some Gaussian diffusion η0 as the weak limit of ηϵ, suitable differential operators Ai, and a positive integer s depending on the smoothness of F.

Keywords: Weak convergence; Locally infinitely divisible; Compensating operator; Historical processes (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:1:p:131-155

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DOI: 10.1016/j.spa.2012.08.012

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