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 $R^d$.File in questo prodotto:
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