Jump processes as generalized gradient flows
Mark A. Peletier, Riccarda Rossi, Giuseppe Savaré, Oliver Tse
2022Institutional Research Information System (Università degli Studi di Brescia)28 citationsDOIOpen Access 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.
Topics & Concepts
MathematicsJumpPure mathematicsMathematical analysisPhysicsQuantum mechanicsGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsPoint processes and geometric inequalities