PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE

doi:10.1007/s10473-019-0302-7

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (3): 629-644.doi: 10.1007/s10473-019-0302-7

PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE

李贺宇¹, 陈夏^1,2

1. School of Mathematics, Jilin University, Changchun 130012, China;
2. Department of Mathematics, University of Tennessee, Knoxville TN 37996, USA

收稿日期:2018-01-27 出版日期:2019-06-25 发布日期:2019-06-27
通讯作者: Xia CHEN E-mail:xchen@math.utk.edu.cn
作者简介:Heyu LI,E-mail:heyul15@mails.jlu.edu.cn
基金资助:
Research partially supported by the "1000 Talents Plan" from Jilin University, Jilin Province and Chinese Government, and by the Simons Foundation (244767).

PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE

Heyu LI¹, Xia CHEN^1,2

1. School of Mathematics, Jilin University, Changchun 130012, China;
2. Department of Mathematics, University of Tennessee, Knoxville TN 37996, USA

Received:2018-01-27 Online:2019-06-25 Published:2019-06-27
Contact: Xia CHEN E-mail:xchen@math.utk.edu.cn
Supported by:
Research partially supported by the "1000 Talents Plan" from Jilin University, Jilin Province and Chinese Government, and by the Simons Foundation (244767).

摘要/Abstract

摘要： This article establishes the precise asymptotics
Eu^m(t, x) (t→∞ or m→∞)
for the stochastic heat equation

with the time-derivative Gaussian noise W/t (t, x) that is fractional in time and homogeneous in space.

关键词: Stochastic heat equation, time-derivative Gaussian noise, Brownian motion, Feynman-Kac representation, Schilder's large deviation

Abstract: This article establishes the precise asymptotics
Eu^m(t, x) (t→∞ or m→∞)
for the stochastic heat equation

with the time-derivative Gaussian noise W/t (t, x) that is fractional in time and homogeneous in space.

Key words: Stochastic heat equation, time-derivative Gaussian noise, Brownian motion, Feynman-Kac representation, Schilder's large deviation

中图分类号:

60J65

李贺宇, 陈夏. PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE[J]. 数学物理学报(英文版), 2019, 39(3): 629-644.

Heyu LI, Xia CHEN. PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE[J]. Acta mathematica scientia,Series B, 2019, 39(3): 629-644.

[1]	陈乐, Kunwoo KIM. NONLINEAR STOCHASTIC HEAT EQUATION DRIVEN BY SPATIALLY COLORED NOISE: MOMENTS AND INTERMITTENCY[J]. 数学物理学报(英文版), 2019, 39(3): 645-668.
[2]	胡耀忠, Khoa LÊ. JOINT HÖLDER CONTINUITY OF PARABOLIC ANDERSON MODEL[J]. 数学物理学报(英文版), 2019, 39(3): 764-780.
[3]	胡耀忠, 刘阳辉, Samy TINDEL. ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE[J]. 数学物理学报(英文版), 2019, 39(3): 669-690.
[4]	Johanna GARZÓN, Samy TINDEL, Soledad TORRES. EULER SCHEME FOR FRACTIONAL DELAY STOCHASTIC DIFFERENTIAL EQUATIONS BY ROUGH PATHS TECHNIQUES[J]. 数学物理学报(英文版), 2019, 39(3): 747-763.
[5]	胡耀忠. SOME RECENT PROGRESS ON STOCHASTIC HEAT EQUATIONS[J]. 数学物理学报(英文版), 2019, 39(3): 874-914.
[6]	韩月才, 孙一芳. SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS[J]. 数学物理学报(英文版), 2018, 38(2): 681-694.
[7]	刘俊峰, Ciprian A. TUDOR. STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE: EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY[J]. 数学物理学报(英文版), 2017, 37(6): 1545-1566.
[8]	申广君, 尹修伟, 闫理坦. ERRATUM TO:LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION[J]. 数学物理学报(英文版), 2017, 37(4): 1173-1176.
[9]	崔静, 闫理坦. CONTROLLABILITY OF NEUTRAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION[J]. 数学物理学报(英文版), 2017, 37(1): 108-118.
[10]	申广君, 尹修伟, 闫理坦. LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION[J]. 数学物理学报(英文版), 2016, 36(2): 394-408.
[11]	申广君, 闫理坦, 刘俊峰. POWER VARIATION OF SUBFRACTIONAL BROWNIAN MOTION AND APPLICATION[J]. 数学物理学报(英文版), 2013, 33(4): 901-912.
[12]	申广君, 陈超, 闫理坦. REMARKS ON SUB-FRACTIONAL BESSEL PROCESSES[J]. 数学物理学报(英文版), 2011, 31(5): 1860-1876.
[13]	胡耀忠, Nualart David, 肖炜麟, 张卫国. EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION[J]. 数学物理学报(英文版), 2011, 31(5): 1851-1859.
[14]	胡耀忠. AN ENLARGEMENT OF FILTRATION FOR BROWNIAN MOTION[J]. 数学物理学报(英文版), 2011, 31(5): 1671-1678.
[15]	汪宝彬. CONVERGENCE RATE OF MULTIPLE FRACTIONAL STRATONOVICH TYPE INTEGRAL FOR HURST PARAMETER LESS THAN 1/2[J]. 数学物理学报(英文版), 2011, 31(5): 1694-1708.

PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE

PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10