Side boundary conditions for a Kolmogorov Diffusion
Event details
Date | 18.12.2023 |
Hour | 15:00 › 16:00 |
Speaker | Richard Sowers (Illinois) |
Location | |
Category | Conferences - Seminars |
Event Language | English |
Abstract:
We consider a Kolmogorov-type PDE corresponding to a particle under white noise force. We are interested in stopping the process at a fixed position, i.e., imposing Dirichlet conditions at a side boundary. We construct a simple Gaussian heat kernel inside the domain, and investigate a boundary-layer kernel, connected to some work by McKean. We show that this boundary layer heat kernel has a novel jump condition. We outline a polynomial expansion of for the heat kernels, and then construct a Volterra equation for solving the original problem. The novel jump leads to a periodic structure of the Volterra equation.
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