In this paper we prove the existence and uniqueness for the solution to a stochastic reaction-diffusion equation, defined on a network, and subjected to nonlocal dynamic stochastic boundary conditions. The result is obtained by deriving a Gaussian-type estimate for the related leading semigroup, under rather mild regularity assumptions on the coefficients. An application of the latter to a stochastic optimal control problem on graphs, is also provided.

Gaussian estimates on networks with dynamic stochastic boundary conditions / Cordoni, F.; Di Persio, L.. - In: INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS. - ISSN 0219-0257. - 20:1(2017), p. 1750001. [10.1142/S0219025717500011]

Gaussian estimates on networks with dynamic stochastic boundary conditions

Cordoni F.;Di Persio L.
2017

Abstract

In this paper we prove the existence and uniqueness for the solution to a stochastic reaction-diffusion equation, defined on a network, and subjected to nonlocal dynamic stochastic boundary conditions. The result is obtained by deriving a Gaussian-type estimate for the related leading semigroup, under rather mild regularity assumptions on the coefficients. An application of the latter to a stochastic optimal control problem on graphs, is also provided.
1
Cordoni, F.; Di Persio, L.
Gaussian estimates on networks with dynamic stochastic boundary conditions / Cordoni, F.; Di Persio, L.. - In: INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS. - ISSN 0219-0257. - 20:1(2017), p. 1750001. [10.1142/S0219025717500011]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/322954
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