Open Access
October, 1995 Explicit Stochastic Integral Representations for Historical Functionals
Steven N. Evans, Edwin A. Perkins
Ann. Probab. 23(4): 1772-1815 (October, 1995). DOI: 10.1214/aop/1176987803


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.


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Steven N. Evans. Edwin A. Perkins. "Explicit Stochastic Integral Representations for Historical Functionals." Ann. Probab. 23 (4) 1772 - 1815, October, 1995.


Published: October, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0852.60062
MathSciNet: MR1379168
Digital Object Identifier: 10.1214/aop/1176987803

Primary: 60H05
Secondary: 60G57 , 60J80

Keywords: Clark's formula , Historical process , martingale measure , predictable representation , stochastic integral , Superprocess , Wiener Chaos

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 4 • October, 1995
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