Annals of Probability

Generalized self-intersection local time for a superprocess over a stochastic flow

Aaron Heuser

Full-text: Open access

Abstract

This paper examines the existence of the self-intersection local time for a superprocess over a stochastic flow in dimensions $d\leq3$, which through constructive methods, results in a Tanaka-like representation. The superprocess over a stochastic flow is a superprocess with dependent spatial motion, and thus Dynkin’s proof of existence, which requires multiplicity of the log-Laplace functional, no longer applies. Skoulakis and Adler’s method of calculating moments is extended to higher moments, from which existence follows.

Article information

Source
Ann. Probab., Volume 40, Number 4 (2012), 1483-1534.

Dates
First available in Project Euclid: 4 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.aop/1341401142

Digital Object Identifier
doi:10.1214/11-AOP653

Mathematical Reviews number (MathSciNet)
MR2978131

Zentralblatt MATH identifier
1278.60126

Subjects
Primary: 60J68: Superprocesses 60G57: Random measures
Secondary: 60H15: Stochastic partial differential equations [See also 35R60] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Superprocess stochastic flow self-intersection local time

Citation

Heuser, Aaron. Generalized self-intersection local time for a superprocess over a stochastic flow. Ann. Probab. 40 (2012), no. 4, 1483--1534. doi:10.1214/11-AOP653. https://projecteuclid.org/euclid.aop/1341401142


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