A Superprocess with a Disappearing Self-Interaction

Abstract

We start with a system of independent branching Brownian motions which, properly organized and normalised, generate a super Brownian motion in the high density limit. We introduce a weak interaction between the particles, that affects the diffusion but not the branching. The interaction is chosen in such a way that the infinite density limit is absolutely continuous with respect to the non-interacting system. We find that, despite the fact that the interaction mechanism never completely disappears, the limiting superprocesses are identical. We study what actually happens to the interaction mechanism, or ghost-process.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1993
Accession Number
ADA274647

Entities

People

  • Lidia Ivanitskaya
  • Robert J. Adler

Organizations

  • Technion – Israel Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Convergence
  • Diffusion
  • Engineering
  • High Density
  • Industrial Engineering
  • Intervals
  • Markov Processes
  • Notation
  • Particles
  • Probability
  • Random Variables
  • Sequences
  • Standards
  • Time Intervals
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.