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Semilinear SPDE driven by a fractional Brownian motion with Hurst parameter H in (0,1/2)

Buckdahn, R (Brest)
Wednesday 06 January 2010, 16:30-17:30

Seminar Room 1, Newton Institute


The talk studies semilinear SPDE driven by a fractional Brownian motion B with Hurst parameter H in (0,1/2). The main tool of their investigation consists in the description of their solutions by a backward doubly stochastic differential equation, driven by B as well as an independent classical Brownian motion W. By applying the techniques of the anticipative Girsanov transformation developed by R.Buckdahn (1992) and translated recently to fractional Brownian motions by Y.Jien and J.Ma (2009) this backward doubly stochastic differential equation can be reduced to a pathwise classical backward stochastic equation driven by W. It describes the viscosity solution to a pathwise PDE which, by Girsanov transformation with respect to B, is related with the original semilinear SPDE driven by the fractional Brownian motion B.

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