Anticipative backward stochastic differential equations driven by fractional Brownian motion

We study the anticipative backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H greater than 1/2. The stochastic integral used throughout the paper is the divergence operator type integral. We obtain the existence and uniqueness of solutions to these equations. A comparison theorem for this type of anticipative BSDEs is also established.Comment: 13 pages, Statistics and Probability Letters (2016

Forward integration, convergence and nonadapted pointwise multipliers

In this paper we study the forward integral of operator-valued processes with respect to a cylindrical Brownian motion. In particular, we provide conditions under which the approximating sequence of processes of the forward integral, converges to the stochastic integral process with respect to Sobolev norms of smoothness alpha < 1/2. This result will be used to derive a new integration by parts formula for the forward integral.Comment: Minor revision. Accepted for publication in Infin. Dimens. Anal. Quantum Probab. Relat. To