Calculus of Variations and Geometric Measure Theory
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M. A. Peletier - R. Rossi - G. Savaré - O. Tse

Jump processes as Generalized Gradient Flows

created by tse on 19 Jun 2020

[BibTeX]

Submitted Paper

Inserted: 19 jun 2020

Year: 2020

ArXiv: 2006.10624 PDF

Abstract:

We have created a functional framework for a class of non-metric gradient systems. The state space is a space of nonnegative measures, and the class of systems includes the Forward Kolmogorov equations for the laws of Markov jump processes on Polish spaces. This framework comprises a definition of a notion of solutions, a method to prove existence, and an archetype uniqueness result. We do this by using only the structure that is provided directly by the dissipation functional, which need not be homogeneous, and we do not appeal to any metric structure.

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