The University of Arizona
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A probabilistic view of the pantograph equation

Mathematical Physics and Probability Seminar

A probabilistic view of the pantograph equation
Series: Mathematical Physics and Probability Seminar
Location: MATH 402
Presenter: Ed Waymire, Oregon State University

Probability theory and differential equations share a long history.  Classical connections may be viewed in terms of probabilistic constructions of Markov processes and the associated Cauchy problem of semigroup theory. A well-known benefit of this connection is in the analysis of well-posedness problems for the differential equation in terms of certain critical phenomena, e.g., stochastic explosion,  associated with the Markov process. In this talk the linear pantograph equation will be introduced and analyzed from two ostensibly different probabilistic perspectives (i) classical Markov process theory (ii) contemporary probability on trees. The origins and overall richness of the pantograph differential equation for analysis and applications is well illustrated by the rather comprehensive treatment by Kato,T. and J.B. McLeod (1971), Bull. AMS, 891-937, and the more recent expository article by Shapira, A. and M. Tyomkyn (2021), MAA Monthly, 630-639, and references therein. This talk is based on ongoing joint work with Radu Dascaliuc, Tuan Pham, and Enrique Thomann, with special thanks to Nick Hale and Andre’ Weideman at Stollenbosch University for bringing it to our attention.

(https://arizona.zoom.us/j/87802949465)