White-noise approach to stochastic integration for a Poisson random measure. (English. Ukrainian original) Zbl 0940.60070

Kaminskyj, A. B.

Theory Probab. Math. Stat. 57, 43-52 (1998); translation from Teor. Jmovirn. Mat. Stat. 57, 41-50 (1997).

The author proposes a construction of the extended stochastic integral with respect to a Poisson random measure which is based on a white-noise approach. Relations of this integral with the Kabanov-Skorokhod integral are studied. It is shown that in the case of a standard Poisson process this integral coincides with the integral defined by the limit of the Riemann sums (in the Stratonovich sense).

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60H05	Stochastic integrals
60G57	Random measures
60J65	Brownian motion

Keywords:

stochastic integration; Poisson measure; white-noise analysis