The Annals of Probability

Local Times for Superdiffusions

Stephen M. Krone

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Abstract

In this work we study local times for a class of measure-valued Markov processes known as superprocesses. We begin by deriving analogues of well-known properties of ordinary local times. Then, restricting our attention to a class of superprocesses (which includes the important case of super-Brownian motion), we prove more detailed properties of the local times, such as joint continuity and a global Holder condition. These are then used to obtain path properties of the superprocesses themselves. For example, we compute the Hausdorff dimension of the "level sets" of super-Brownian motion.

Article information

Source
Ann. Probab., Volume 21, Number 3 (1993), 1599-1623.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989133

Digital Object Identifier
doi:10.1214/aop/1176989133

Mathematical Reviews number (MathSciNet)
MR1235431

Zentralblatt MATH identifier
0778.60056

JSTOR
links.jstor.org

Subjects
Primary: 60J55: Local time and additive functionals
Secondary: 60G17: Sample path properties 60G57: Random measures

Keywords
Superprocesses measure-valued processes local times joint continuity Holder continuity path properties Hausdorff dimension

Citation

Krone, Stephen M. Local Times for Superdiffusions. Ann. Probab. 21 (1993), no. 3, 1599--1623. doi:10.1214/aop/1176989133. https://projecteuclid.org/euclid.aop/1176989133


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