Backward Stochastic Variational Inequalities Driven by Fractional Brownian Motion

Details Backward Stochastic Variational Inequalities Driven by Fractional Brownian Motion Backward Stochastic Variational Inequalities Driven by Fractional Brownian Motion

2011-02-15

arxiv.org/abs/1102.3014v2

Mathematics

Probability

20 pages

Scientific paper

We study, in the framework of fractional stochastic calculus, the existence and uniqueness of the solution for a multivalued backward stochastic differential equation, formally written as: \[[c]{l}% dY(t)+f(t,\eta(t),Y(t),Z(t))dt\in\partial\phi(Y(t))dt+Z(t)dB^{H}(t),\quad0\leq t\leq T, Y(T)=\xi.\] where $\eta$ is a stochastic processes given by $\eta(t) =\eta(0) +b(t) +\int_{0}^{t}\sigma(s) dB^{H}(s)$, $\partial\phi$ is a multivalued operator of subdifferential type and $B^{H}$ is a fractional Brownian motion with Hurst parameter greater than $1/2.$ The stochastic integral use throughout this paper is the divergence operator type integral. We envisage the connections between this solution and the solution of parabolic multivalued partial differential equation, too.

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