ON MULTIPLE POISSON STOCHASTIC INTEGRALS AND ASSOCIATED
MARKOV SEMIGROUPS

Abstract: Multiple stochastic integrals (m.s.i.)

with respect to the centered Poisson random measure

are discussed, where

is a measurable space. A ”diagram
formula” for evaluation of products of (Poisson) m.s.i. as sums of m.s.i. is derived. With a
given contraction semigroup

in

we associate a semigroup

in

by the relation

and
prove that

is Markov if and only if

is doubly sub-Markov; the
corresponding Markov process can be described as time evolution (with immigration) of the
(infinite) system of particles, each moving independently according to

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -