Side boundary conditions for a Kolmogorov Diffusion


Event details

Date 18.12.2023
Hour 15:0016:00
Speaker Richard Sowers (Illinois)
Category Conferences - Seminars
Event Language English


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.


Practical information

  • Expert
  • Free




probability and stochastic analysis Seminar

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