We study the existence and regularity of the density for the solution u(t,x) (with fixed t > 0 and x D) of the heat equation in a bounded domain D aS' d driven by a stochastic inhomogeneous Neumann boundary condition with stochastic term. The stochastic perturbation is given by a fractional Brownian motion process. Under suitable regularity assumptions on the coefficients, by means of tools from the Malliavin calculus, we prove that the law of the solution has a smooth density with respect to the Lebesgue measure in.

Absolute continuity of the law for solutions of stochastic differential equations with boundary noise

Zanella M.
2017-01-01

Abstract

We study the existence and regularity of the density for the solution u(t,x) (with fixed t > 0 and x D) of the heat equation in a bounded domain D aS' d driven by a stochastic inhomogeneous Neumann boundary condition with stochastic term. The stochastic perturbation is given by a fractional Brownian motion process. Under suitable regularity assumptions on the coefficients, by means of tools from the Malliavin calculus, we prove that the law of the solution has a smooth density with respect to the Lebesgue measure in.
2017
density of the solution
Fractional Brownian motion
stochastic boundary condition
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1150008
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