Asymptotic expansions in limit theorems for stochastic processes. II
成果类型：
Article
署名作者：
Wentzell, AD
署名单位：
Tulane University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s004400050207
发表日期：
1999
页码：
255-271
关键词：
摘要：
For a certain class of families of stochastic processes eta(epsilon)(t), 0 less than or equal to t less than or equal to T, constructed starting from sums of independent random variables, limit theorems for expectations of functionals F(eta(epsilon)[0, T]) are proved of the form EF(eta(epsilon)[0, T]) = E[F(omega(0)[0,T]) + (i=1)Sigma(m) epsilon(j/2) . A(i)F(omega(0)[0,T])] + o(epsilon(m/2)) (epsilon down arrow 0), where omega(0) is a Wiener process starting from 0, with variance sigma(2) per unit time, Ai 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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