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Asymptotic expansions in limit theorems for stochastic processes. I
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  • Published: November 1996

Asymptotic expansions in limit theorems for stochastic processes. I

  • A. D. Wentzell1 

Probability Theory and Related Fields volume 106, pages 331–350 (1996)Cite this article

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Summary.

For some families of locally infinitely divisible Markov processes η ɛ (t), 0≦ t≦ T, with frequent small jumps, limit theorems for expectations of functionals F(η ɛ [0,T]) are proved of the form

| E ɛ F(η ɛ [0,T])−E 0 F(η 0 [0,T])|≦ const ⋅ k(ɛ) ,

E ɛ F(η ɛ [0,T])=E 0 [F(η 0 [0,T])+ k(ɛ) ⋅ A 1 F(η 0 [0,T])]+o(k(ɛ))  (ɛ↓ 0) ,

where A 1 is a linear differential operator acting on functionals, and the constant is expressed in terms of the local characteristics of the processes η ɛ (t) and the norms of the derivatives of the functional F.

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Authors and Affiliations

  1. Department of Mathematics, Tulane University, New Orleans, LA 70118, USA, , , , , , US

    A. D. Wentzell

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  1. A. D. Wentzell
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Received: 1 April 1994 / In revised form: 30 September 1995

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Wentzell, A. Asymptotic expansions in limit theorems for stochastic processes. I. Probab Theory Relat Fields 106, 331–350 (1996). https://doi.org/10.1007/s004400050067

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  • Issue Date: November 1996

  • DOI: https://doi.org/10.1007/s004400050067

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  • Mathematics Subject classification (1991):  60F17
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