The stochastic value function in metric measure spaces

Ugo Bessi

doi:10.3934/dcds.2017076

Article Contents

2017, Volume 37, Issue 4: 1819-1839. Doi: 10.3934/dcds.2017076

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The stochastic value function in metric measure spaces

Ugo Bessi

Dipartimento di Matematica, Università di Roma Tre, Largo S. Leonardo Murialdo 1,00146 Roma, Italy

Author Bio: E-mail address: bessi@mat.uniroma3.it

Received: March 31, 2016

Revised: October 31, 2016

Published: May 2017

Work partially supported by the PRIN2009 grant "Critical Point Theory and Perturbative Methods for Nonlinear Differential Equations.

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Abstract

Let $(S,d)$ be a compact metric space and let $m$ be a Borel probability measure on $(S,d)$ . We shall prove that, if $(S,d,m)$ is a $RCD(K,\infty)$ space, then the stochastic value function satisfies the viscous Hamilton-Jacobi equation, exactly as in Fleming's theorem on ${\bf{R}}^d$ .

Keywords:

Viscous Hamilton-Jacobi equation,
metric measure spaces.

Mathematics Subject Classification: Primary:49L20, 49L25.

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