2014/10/03 by Xuebin Lü, Xuebin Lu, Lu, Xuebin +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60E07 #60G20 #60G51 #60G52 #60H40 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #math-ph #math.AP #math.DS #math.MP #math.PR #math.ST #msc:60E07 #msc:60G20 #msc:60G51 #msc:60G52 #msc:60H40 #stat.TH
paper · pdf · doi:10.48550/arxiv.1410.0992
17 pages. arXiv admin note: text overlap with arXiv:1307.4173
arxiv created 2014/10/03 · openalex publication_date 2014/10/03 · arxiv updated 2014/10/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we investigate stochastic partial differential equations driven by multi-parameter anisotropic fractional Levy noises, including the stochastic Poisson equation, the linear heat equation, and the quasi-linear heat equation. Well-posedness of these equations under the fractional noises will be addressed. The multi-parameter anisotropic fractional Levy noise is defined as the formal derivative of the anisotropic fractional Levy random field. In doing so, there are two folds involved. First, we consider the anisotropic fractional Levy random field as the generalized functional of the path of the pure jump Levy process. Second, we build the Skorohod integration with respect to the multi-parameter anisotropic fractional Levy noise by white noise approach.