AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

On the Martingale Problem for Interactive Measure-Valued Branching Diffusions
Edwin Perkins
SEARCH THIS BOOK:

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$39
Individual Members: US$23.40
Institutional Members: US$31.20
Order Code: MEMO/115/549
[Add Item]

Request Permissions

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.

Readership

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
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia