On the martingale problem for interactive measure-valued branching diffusions / Edwin Perkins.

Format:

Book

Author/Creator:

Perkins, Edwin Arend, 1953- author.

Series:

Memoirs of the American Mathematical Society ; Volume 115, Number 549.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 115, Number 549

Language:

English

Subjects (All):

Branching processes.

Random measures.

Stochastic analysis.

Physical Description:

1 online resource (102 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island, United States : American Mathematical Society, 1995.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""1. Introduction""; ""2. Historical Integrals and Stochastic Calculus""; ""3. On the Compact Support Property""; ""4. Pathwise Existence and Uniqueness in a Stochastic Equation for Historical Processes""; ""5. Existence and Uniqueness for a Historical Martingale Problem""; ""References""

Notes:

"May 1995, Volume 115, Number 549 (first of 5 numbers)"--Cover.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0128-2