A stochastic differential equation for local times of super-Brownian motion
Jean-Fran\c{c}ois Le Gall, Edwin Perkins
TL;DR
This paper derives an explicit stochastic differential equation describing the local times of super-Brownian motion, using excursion theory and superprocess tools, advancing understanding of these complex stochastic processes.
Contribution
It introduces a novel stochastic differential equation characterizing local times of super-Brownian motion, linking excursion theory with superprocess analysis.
Findings
Derived explicit SDE for local times
Connected local times with excursion theory
Enhanced understanding of super-Brownian motion
Abstract
We show that local times of super-Brownian motion, or of Brownian motion indexed by the Brownian tree, satisfy an explicit stochastic differential equation. Our proofs rely on both excursion theory for the Brownian snake and tools from the theory of superprocesses.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Theoretical and Computational Physics