dc.contributor.author Hu, Yaozhong dc.contributor.author Oksendal, Bernt dc.contributor.author Zhang, Tusheng dc.date.accessioned 2005-04-14T17:51:09Z dc.date.available 2005-04-14T17:51:09Z dc.date.issued 2004 dc.identifier.citation Hu, YZ; Oksendal, B; Zhang, TS. General fractional multiparameter white noise theory and stochastic partial differential equations. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. 2004.29:1-23 dc.identifier.other ISI:000220035100001 dc.identifier.uri http://hdl.handle.net/1808/282 dc.description.abstract We present a white noise calculus for d-parameter fractional Brownian motion B-H (x, omega); x is an element of R-d, omega is an element of Omega with general d-dimensional Hurst parameter H = (H-l,..., H-d) is an element of (0, 1)(d). As an illustration we solve the stochastic Poisson problem DeltaU(x) = -W-H(x); x is an element of D, U = 0 on partial derivativeD, where the potential W-H(x) is d-parameter fractional white noise given by W-H (x) = (partial derivative(d) B-H (x)) / (partial derivativex(l)...partial derivativex(d)), and D subset of R-d is a given bounded smooth domain. We also solve the linear stochastic heat equation (partial derivativeU/partial derivativet)(t, x) = 1/2 DeltaU(t, x) + W-H (t, x). For each equation we give sufficient conditions that the solutions U(x) and U(t,x), respectively, are square integrable random variables for all t, x. dc.format.extent 282181 bytes dc.format.mimetype application/pdf dc.language.iso en_US dc.publisher MARCEL DEKKER INC dc.subject Multi-parameter fractional brownian motion dc.subject Fractional white noise calculus dc.subject Stochastic poisson equation dc.subject Stochastic heat equation dc.title General fractional multiparameter white noise theory and stochastic partial differential equations dc.type Preprint dc.identifier.doi 10.1081/PDE-120028841 dc.rights.accessrights openAccess
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