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⊂ℝ^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 ℝ.

Absolute continuity of the law for solutions of stochastic differential equations with boundary noise / Bonaccorsi, Stefano; Zanella, Margherita. - In: STOCHASTICS AND DYNAMICS. - ISSN 0219-4937. - 2017, 17:6(2017). [10.1142/S0219493717500459]

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

Bonaccorsi, Stefano;
2017

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⊂ℝ^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 ℝ.
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Bonaccorsi, Stefano; Zanella, Margherita
Absolute continuity of the law for solutions of stochastic differential equations with boundary noise / Bonaccorsi, Stefano; Zanella, Margherita. - In: STOCHASTICS AND DYNAMICS. - ISSN 0219-4937. - 2017, 17:6(2017). [10.1142/S0219493717500459]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/193427
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