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: -