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The stochastic value function in metric measure spaces

  • Author Bio: E-mail address: bessi@mat.uniroma3.it
Work partially supported by the PRIN2009 grant "Critical Point Theory and Perturbative Methods for Nonlinear Differential Equations.
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  • 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 ${\bf{R}}^d$ .

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


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