Explicit stochastic integral representations for historical functionals

• 成果类型: Article
• 署名作者: Evans, SN; Perkins, EA
• 署名单位: University of British Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176987803
• 发表日期: 1995
• 页码: 1772-1815
• 关键词: diffusion-processes; branching-processes; local-times; superprocesses

摘要

It is known from previous work of the authors that any square-integrable functional of a superprocess may be represented as a constant plus a stochastic integral against the associated orthogonal martingale measure. Here we give, for a large class of such functionals, an explicit description of the integrand that is analogous to Clark's formula for the representation of certain Brownian functionals. As a consequence, we develop a partial analogue of the Wiener chaos expansion in the superprocess setting. Rather than work with superprocesses per se, our results are stated and proved in the richer and more natural context of the associated historical process.