Gaussian estimates on networks with dynamic stochastic boundary conditions

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. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0219025717500011