On the chaotic character of the stochastic heat equation, II

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109258

Title:	On the chaotic character of the stochastic heat equation, II
Authors:	須上苑;Conus, Daniel;Joseph, Mathew;Khoshnevisan, Davar;Shiu, Shang-Yuan
Contributors:	理學院數學系
Keywords:	Correlation;Economics;Exponents;Finance;Fluctuation;Gaussian;Heat;Heat equations;Insurance;Management;Mathematical analysis;Mathematical and Computational Biology;Mathematical and Computational Physics;Mathematics;Mathematics and Statistics;Noise;Nonlinear equations;Operations Research/Decision Theory;Probability;Probability theory;Probability Theory and Stochastic Processes;Quantitative Finance;Random noise;Spacetime;Statistics for Business;Stochastic models;Stochasticity;Studies;Theoretical;Thermodynamics;Viscosity
Date:	2013-08-01
Issue Date:	2026-04-23 16:19:08 (UTC+8)
Publisher:	Springer New York;Berlin/Heidelberg: Springer Berlin Heidelberg
Abstract:	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
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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