TY - JOUR
T1 - Jump processes as generalized gradient flows
AU - Peletier, Mark A.
AU - Rossi, Riccarda
AU - Savaré, Giuseppe
AU - Tse, Oliver
N1 - Funding Information:
M.A.P. acknowledges support from NWO Grant 613.001.552, “Large Deviations and Gradient Flows: Beyond Equilibrium". R.R. and G.S. acknowledge support from the MIUR - PRIN project 2017TEXA3H “Gradient flows, Optimal Transport and Metric Measure Structures". G.S. also acknowledges the support of the Institute of Advanced Study of the Technical University of Munich, of IMATI-CNR, Pavia, and of the Department of Mathematics of the University of Pavia, where this project was partially carried out. O.T. acknowledges support from NWO Vidi grant 016.Vidi.189.102, “Dynamical-Variational Transport Costs and Application to Variational Evolutions". Finally, the authors thank Jasper Hoeksema for insightful and valuable comments during the preparation of this manuscript.
PY - 2022/2
Y1 - 2022/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85122335516&partnerID=8YFLogxK
U2 - 10.1007/s00526-021-02130-2
DO - 10.1007/s00526-021-02130-2
M3 - Article
AN - SCOPUS:85122335516
SN - 0944-2669
VL - 61
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 1
M1 - 33
ER -