Multiple Integration with Respect to Poisson and Levy Processes.

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.

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1988
Accession Number
ADA192895

Entities

People

  • Jerzy Szulga
  • Olav Kallenberg

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Convergence
  • Decoupling
  • Integrals
  • Mathematics
  • Probability
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.