Directed chain stochastic differential equation with reflection

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• Tomoyuki Ichiba (University of California, Santa Barbara)
• Friday 09 August 2024, 09:00-10:00
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SSDW02 - Stochastic reflection

In this talk we shall discuss stochastic processes interacting on infinite directed graph by a class of stochastic differential equations with local times and marginal distribution constraints. Here, the local times describes the reflection  of the process on the boundary at each node and the marginal distribution constraints provide the uniqueness of the distribution. We start with a system of finite-dimensional stochastic equations for the vertices in the finite directed graph to discuss existence and uniqueness of the system and then take its limits as we let the number of vertices go to infinity. We shall discuss the stability property of such systems. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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