An entropy generation formula on $$\varvec{RCD(K,\infty )}$$ R C D ( K , ∞ ) spaces

An entropy generation formula on $$\varvec{RCD(K,\infty )}$$ R C D ( K , ∞ ) spaces J. Feng and T. Nguyen have shown that the solutions of the Fokker–Planck equation in $$\mathbf{R}^d$$ R d satisfy an entropy generation formula. We prove that, in compact metric measure spaces with the $$RCD(K,\infty )$$ R C D ( K , ∞ ) property, a similar result holds for curves of measures whose density is bounded away from zero and infinity. We use this fact to show the existence of minimal characteristics for the stochastic value function. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Differential Equations and Applications NoDEA Springer Journals

An entropy generation formula on $$\varvec{RCD(K,\infty )}$$ R C D ( K , ∞ ) spaces

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis
ISSN
1021-9722
eISSN
1420-9004
D.O.I.
10.1007/s00030-018-0518-6
Publisher site
See Article on Publisher Site

Abstract

J. Feng and T. Nguyen have shown that the solutions of the Fokker–Planck equation in $$\mathbf{R}^d$$ R d satisfy an entropy generation formula. We prove that, in compact metric measure spaces with the $$RCD(K,\infty )$$ R C D ( K , ∞ ) property, a similar result holds for curves of measures whose density is bounded away from zero and infinity. We use this fact to show the existence of minimal characteristics for the stochastic value function.

Journal

Nonlinear Differential Equations and Applications NoDEASpringer Journals

Published: Jun 5, 2018

References

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