Diffusion processes

Thursday, May 10, 2018 - 10:00am - 10:50am
William McEneaney (University of California, San Diego)
Stationary-action approaches to solution of two-point boundary problems (TPBVPs) for conservative systems and stationarity-based approaches to representations for solutions of Schrödinger initial value problems are closely related.
Thursday, June 25, 2015 - 4:05pm - 5:05pm
Amarjit Budhiraja (University of North Carolina, Chapel Hill)
An asymptotic framework for optimal control of multiclass stochastic processing networks, using formal diffusion approximations under suitable temporal and spatial scaling, by Brownian control problems (BCP) and their equivalent workload formulations (EWF), has been developed by Harrison (1988). This framework has been implemented in many works for constructing asymptotically optimal control policies for a broad range of stochastic network models.
Thursday, June 25, 2015 - 2:45pm - 3:45pm
Kavita Ramanan (Brown University)
Two approaches to characterizing reflected diffusions include the submartingale problem formulation or a formulation in terms of the Skorokhod problem and stochastic differential equations. We introduce these formulations for a large class of piecewise smooth domains and, under suitable assumptions, we show that well-posedness of the submartingale problem is equivalent to existence and uniqueness in law of weak solutions to the corresponding stochastic differential equation with reflection.
Wednesday, September 26, 2012 - 10:15am - 11:05am
Marek Fila (Comenius University in Bratislava)
We consider positive solutions of the Cauchy problem for the fast diffusion equation. Sufficient conditions for extinction of solutions in finite time are well known. We shall discuss results on the asymptotic behavior of solutions near the extinction time obtained in collaboration with John R. King, Juan Luis Vazquez, Michael Winkler and Eiji Yanagida.
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