Stochastic flows related to Walsh Brownian motion
Hatem Hajri
TL;DR
This paper extends the Tanaka and skew Brownian motion equations to simple graphs, classifies all solutions using transition kernel theory, and explores stochastic flows related to Walsh Brownian motion.
Contribution
It introduces a new equation on graphs extending classical stochastic processes and classifies solutions via transition kernels, advancing the understanding of Walsh Brownian motion.
Findings
All solutions can be classified by probability measures.
The extended equation generalizes Tanaka and skew Brownian motion.
Application of Le Jan and Raimond's transition kernel theory.
Abstract
We define an equation on a simple graph which is an extension of Tanaka equation and the skew Brownian motion equation. We then apply the theory of transition kernels developped by Le Jan and Raimond and show that all the solutions can be classified by probability measures.
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Random Matrices and Applications