Stochastic partial differential equations driven by multiparameter fractional white noise (Q2702398)

The authors develop a multiparameter white noise theory for fractional Brownian motions in \(\mathbb R^d\) with Hurst multiparameter \(H=(H_1,\ldots,H_d)\in (1/2,1)^d\). The result generalizes an older result of the authors [``Fractional white noise calculus and application to finance'' (Preprint, University of Oslo, 1999)] which covers the case \(d=1\). In both articles the Wick product is used to define the stochastic integral. The theory is applied to the Poisson equation driven by multiparameter fractional white noise. They show unique existence of a solution and give conditions, which imply that this solution is a classical one. The results are compared to the standard white noise case.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00049].