Limit theorems with asymptotic expansions for stochastic processes

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.

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Year of publication:	2013
Authors:	Yang, Xiangfeng
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 123.2013, 1, p. 131-155
Publisher:	Elsevier
Subject:	Weak convergence \| Locally infinitely divisible \| Compensating operator \| Historical processes

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011065074