Memoirs of the American Mathematical Society 1995; 89 pp; softcover Volume: 115 ISBN10: 0821803581 ISBN13: 9780821803585 List Price: US$39 Individual Members: US$23.40 Institutional Members: US$31.20 Order Code: MEMO/115/549
 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 Girsanovtype theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measurevalued diffusions (superprocesses) is well posed. The resulting measurevalued 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
