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

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

李贺宇1, 陈夏1,2   

  1. 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 CHEN1,2   

  1. 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: This article establishes the precise asymptotics
Eum(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
Eum(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