Gaussian estimates on networks with dynamic stochastic boundary conditions
2017 ◽
Vol 20
(01)
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pp. 1750001
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Keyword(s):
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.
2020 ◽
Vol 379
(3)
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pp. 1001-1034
2007 ◽
Vol 137
(3)
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pp. 497-505
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2016 ◽
Vol 33
(1)
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pp. 67-92
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