Stochastic integral representation of multiplicative operator functionals of a Wiener process

Multiplicative Operator Functionals of a Markov Process

Brownian excursions, stochastic integrals, and representation of Wiener functionals

A stochastic calculus similar to Malliavin’s calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integral representation of square integrable Wiener f...

A characterization of the kernels associated with the multiple integral representation of some functionals of the Wiener process

In this paper we present a characterization of those Wiener functionals that are the likelihood ratio for a 'signal plus independent noise' model. The characterization is expressed in terms of the representation of such functionals in a series of multiple Wiener integrals. Let {ys, 0 <s =z r} be a random process with measurable sample functions satisfying ] y, ] G K as. Let { Ws, 0 <s < T} be a...

Stochastic Integral with respect to Cylindrical Wiener Process

This paper is devoted to a construction of the stochastic Itô integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The connection of the introduced integral with the integral defined by Walsh [9] is provided as well.

Convergence of Integral Functionals of Stochastic Processes

We are grateful to the referees and Benedikt Pötscher for their helpful and constructive comments+ The research of the first author was partially supported by OTKA grants T37668 and T43037 and NSF-OTKA grant INT0223262+ The research of the second author was partially supported by NATO grant PST+EAP+CLG 980599 and NSF-OTKA grant INT-0223262+ Address correspondence to István Berkes, Graz Universi...