General fractional multiparameter white noise theory and stochastic partial differential equations
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 |