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

作者：Bonaccorsi Stefano; Zanella Margherita^*

来源：Stochastics and Dynamics, 2017, 17(6): 1750045.

DOI：10.1142/S0219493717500459

• Fractional Brownian motion
• stochastic boundary condition
• density of the solution

We study the existence and regularity of the density for the solution u(t, x) (with fixed t > 0 and x is an element of D) of the heat equation in a bounded domain D subset of 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.

• 出版日期2017-12