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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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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DOI: https://doi.org/10.1007/s004400050067
- Mathematics Subject classification (1991): 60F17