Abstract
. For a certain class of families of stochastic processes ηε(t), 0≤t≤T, constructed starting from sums of independent random variables, limit theorems for expectations of functionals F(ηε[0,T]) are proved of the form
where w 0 is a Wiener process starting from 0, with variance σ2 per unit time, A i are linear differential operators acting on functionals, and m=1 or 2. Some intricate differentiability conditions are imposed on the functional.
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Received: 12 September 1995 / Revised version: 6 April 1998
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Wentzell, A. Asymptotic expansions in limit theorems for stochastic processes. II. Probab Theory Relat Fields 113, 255–271 (1999). https://doi.org/10.1007/s004400050207
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DOI: https://doi.org/10.1007/s004400050207
- Mathematics Subject Classification (1991): 60F17