On Path Properties of Certain Infinitely Divisible Processes.

Abstract

Sample path properties of Poissonian type stochastic integral processes are studied. It is proven that various properties of the sections of the deterministic kernel (as, for example, unboundedness, discontinuity, etc.) are inherited by the sample paths of the corresponding stochastic integral process. An analogous statement for Gaussian processes is false. As a main tool, a series representation of stochastic integral processes is fully developed and this may be of independent interest. Keywords: Infinitely divisible processes; Symmetry.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1987
Accession Number
ADA192016

Entities

People

  • Jan Rosinski

Organizations

  • University of Tennessee

Tags

DTIC Thesaurus Topics

  • Data Science
  • Gaussian Processes
  • Information Science
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Probability
  • Random Variables
  • Sequences
  • Shot Noise
  • Statistical Analysis
  • Statistics
  • Stochastic Processes
  • Tennessee
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.