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 $R^d$.

Bessi, U. (2017). The stochastic value function in metric measure spaces. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 37(4), 1819-1839 [10.3934/dcds2017076].

The stochastic value function in metric measure spaces

BESSI, Ugo
2017-01-01

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 $R^d$.
2017
Bessi, U. (2017). The stochastic value function in metric measure spaces. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 37(4), 1819-1839 [10.3934/dcds2017076].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/317135
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