The Annals of Probability

Superprocesses in random environments

Leonid Mytnik

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Abstract

We study the limiting behavior of large branching particle systems undergoing random motion, whose branching mechanism is affected by a random environment. The weak convergence result is established for a sequence of such particle systems and the limiting process is characterized as the unique solution of a martingale problem. The proof of uniqueness of the solution for the martingale problem requires an extension of standard duality techniques.

Article information

Source
Ann. Probab., Volume 24, Number 4 (1996), 1953-1978.

Dates
First available in Project Euclid: 6 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1041903212

Digital Object Identifier
doi:10.1214/aop/1041903212

Mathematical Reviews number (MathSciNet)
MR1415235

Zentralblatt MATH identifier
0874.60041

Subjects
Primary: 60G57: Random measures 60F17: Functional limit theorems; invariance principles
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Measure-valued processes superprocess martingale problem duality random environment

Citation

Mytnik, Leonid. Superprocesses in random environments. Ann. Probab. 24 (1996), no. 4, 1953--1978. doi:10.1214/aop/1041903212. https://projecteuclid.org/euclid.aop/1041903212


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