The Annals of Probability
- Ann. Probab.
- Volume 23, Number 4 (1995), 1772-1815.
Explicit Stochastic Integral Representations for Historical Functionals
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.
Ann. Probab., Volume 23, Number 4 (1995), 1772-1815.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H05: Stochastic integrals
Secondary: 60G57: Random measures 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Evans, Steven N.; Perkins, Edwin A. Explicit Stochastic Integral Representations for Historical Functionals. Ann. Probab. 23 (1995), no. 4, 1772--1815. doi:10.1214/aop/1176987803. https://projecteuclid.org/euclid.aop/1176987803