UNIVERSITY
OF WROCŁAW
 
Main Page
Online First
Contents of previous volumes
Forthcoming papers
General Information
Instructions for authors


VOLUMES
41.2 41.1 40.2 40.1 39.2 39.1 38.2
38.1 37.2 37.1 36.2 36.1 35.2 35.1
34.2 34.1 33.2 33.1 32.2 32.1 31.2
31.1 30.2 30.1 29.2 29.1 28.2 28.1
27.2 27.1 26.2 26.1 25.2 25.1 24.2
24.1 23.2 23.1 22.2 22.1 21.2 21.1
20.2 20.1 19.2 19.1 18.2 18.1 17.2
17.1 16.2 16.1 15 14.2 14.1 13.2
13.1 12.2 12.1 11.2 11.1 10.2 10.1
9.2 9.1 8 7.2 7.1 6.2 6.1
5.2 5.1 4.2 4.1 3.2 3.1 2.2
2.1 1.2 1.1 .imap
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 3, Fasc. 2,
pages 217 - 239
 

ON MULTIPLE POISSON STOCHASTIC INTEGRALS AND ASSOCIATED MARKOV SEMIGROUPS

D. Surgailis

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

 (n)      integral 
q  (f) =  X f(x1,...,xn)q(dx1)...q(dxn),  n = l,2,...
           n
with respect to the centered Poisson random measure q(dx), E[q(dx)] = 0, E[(q(dx))] = m(dx), are discussed, where (X, m) 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 At, t > 0, in  2
L (X) we associate a semigroup G(At), t > 0, in   2
L (_O_) by the relation

     (n)              (n)
G(At)q   (f1^ ox  ... ox ^fn) = q  (Atf1^ ox  ...^ ox Atfn)
and prove that G(At), t > 0, is Markov if and only if At, t > 0, 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 At, t > 0.

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

Key words and phrases: -

Download:    Abstract    Full text   Abstract + References