Springer New York;Berlin/Heidelberg: Springer Berlin Heidelberg
摘要:
摘要： Consider the stochastic heat equation , where the solution u := u t ( x ) is indexed by , and is a centered Gaussian noise that is white in time and has spatially-correlated coordinates. We analyze the large- fixed- t behavior of the solution u in different regimes, thereby study the effect of noise on the solution in various cases. Among other things, we show that if the spatial correlation function f of the noise is of Riesz type, that is , then the “fluctuation exponents” of the solution are for the spatial variable and for the time variable, where . Moreover, these exponent relations hold as long as ; that is precisely when Dalang’s theory [Dalang, Electron J Probab 4:(Paper no. 6):29, 1999 ] implies the existence of a solution to our stochastic PDE. These findings bolster earlier physical predictions [Kardar et al., Phys Rev Lett 58(20):889–892, 1985 ; Kardar and Zhang, Phys Rev Lett 58(20):2087–2090, 1987 ]. 其他題名： Probab. Theory Relat. Fields 出版者： Berlin/Heidelberg: Springer Berlin Heidelberg 出版日期： 2013-08 出處： Probability theory and related fields, 2013-08, Vol.156 (3-4), p.483-533 資源來源： EBSCOhost Business Source Premier 版權： Springer-Verlag 2012 版權： Springer-Verlag Berlin Heidelberg 2013 版權： Springer-Verlag 2012. 識別號： ISSN: 0178-8051 識別號： ISSN: 1432-2064 識別號： EISSN: 1432-2064 識別號： DOI: 10.1007/s00440-012-0434-3 識別號： CODEN: PTRFEU
