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On the Martingale Problem for Interactive Measure-Valued Branching Diffusions
Edwin Perkins

Memoirs of the American Mathematical Society
1995; 89 pp; softcover
Volume: 115
ISBN-10: 0-8218-0358-1
ISBN-13: 978-0-8218-0358-5
List Price: US$41
Individual Members: US$24.60
Institutional Members: US$32.80
Order Code: MEMO/115/549
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This book develops stochastic integration with respect to "Brownian trees" and its associated stochastic calculus, with the aim of proving pathwise existence and uniqueness in a stochastic equation driven by a historical Brownian motion. Perkins uses these results and a Girsanov-type theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measure-valued diffusions (superprocesses) is well posed. The resulting measure-valued processes will arise as limits of the empirical measures of branching particle systems in which particles interact through their spatial motions or, to a lesser extent, through their branching rates.


Research mathematicians.

Table of Contents

  • Introduction
  • Historical integrals and stochastic calculus
  • On the compact support property
  • Pathwise existence and uniqueness in a stochastic equation for historical processes
  • Existence and uniqueness for a historical Martingale problem
  • References
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