This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) ...This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) that is fractional in time and homogeneous in space.展开更多
In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the ...In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the preconditioned matrix are given. Our results extend the corresponding ones in [3] and [4].展开更多
In this paper, we first prove Schilder＇s theorem in H？lder norm （0 ≤ α 〈1） with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of...In this paper, we first prove Schilder＇s theorem in H？lder norm （0 ≤ α 〈1） with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for Cr,p-capacity in the stronger topology.展开更多
基金Research partially supported by the “1000 Talents Plan” from Jilin University,Jilin Province and Chinese Governmentby the Simons Foundation(244767)
文摘This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) that is fractional in time and homogeneous in space.
基金Supported by the Natural Science Foundation of Guangdong Province (06025061, 91510224000002)the National Natural Science Foundation of China (10971075, 10671077)the State Key Laboratory of Scientific and Engineering Computing
文摘In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the preconditioned matrix are given. Our results extend the corresponding ones in [3] and [4].
基金Supported by NSFC(Grant Nos.11271013,61273074,61201065,61203219,11471104)the Fundamental Research Funds for the Central Universities,HUST(Grant Nos.2012QN028 and 2014TS066)+2 种基金IRTSTHN(Grant No.14IRSTHN023)Ph D research startup foundation of He’nan Normal University(Grant No.5101019170120)Youth Science Foundation of He’nan Normal University(Grant No.5101019279032)
文摘In this paper, we first prove Schilder＇s theorem in H？lder norm （0 ≤ α 〈1） with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for Cr,p-capacity in the stronger topology.
