On Exponential Changes of Measure for the Feller Diffusion and Superprocesses

Abstract

Let eta be a super process under the measure P. We show the existence of probability measures which are absolutely continuous with respect to P, and whose Radon-Nikodym derivatives are suitably normalized exponential functions of the self intersection local time of eta. These measures correspond to measure valued processes exhibiting a certain amount of self interaction. A finite time divergence of the total mass (1, etat) is shown to occur in a related model in which the change of measure involves the occupation measure of the super process. As an independently interesting side issue we also obtain a number of results related to a self interacting version of the Feller diffusion.

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Document Details

Document Type
Technical Report
Publication Date
Jan 05, 1998
Accession Number
ADA337332

Entities

People

  • Robert J. Adler
  • Srikanth K. Iyer

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Climate Change
  • Computations
  • Delta Functions
  • Differential Equations
  • Diffusion
  • Equations
  • Industrial Engineering
  • Inequalities
  • Integrals
  • Markov Processes
  • Partial Differential Equations
  • Particles
  • Probability
  • Sequences
  • Standards
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.
  • Psychometric Testing or Psychological Assessment.