Accession Number : ADA192895

Title :   Multiple Integration with Respect to Poisson and Levy Processes.

Descriptive Note : Rept. for Sep 87-Aug 88,

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES

Personal Author(s) : Kallenberg, Olav ; Szulga, Jerzy

Report Date : FEB 1988

Pagination or Media Count : 48

Abstract : Necessary and sufficient conditions are given for the existence of a multiple stochastic integral of the form (integral over) fdx1...dXd, where X1,...,Xd are components of a positive or symmetric pure jump type Levy process in R to the dth power. Conditions are also given for a sequence of integrals of this type to converge in probability to zero or infinity, or to be tight. All arguments proceed via reduction to the special case of Poisson integrals. Keywords: Stochastic integrals; Poisson representation; Levy process; Decoupling; Symmetrization; Convergence in probability; Tightness; Completeness.

Descriptors :   *STOCHASTIC PROCESSES, INTEGRALS, POISSON DENSITY FUNCTIONS, SEQUENCES, TIGHTNESS, NUMERICAL INTEGRATION, CONVERGENCE.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE