Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (3): 629-644.doi: 10.1007/s10473-019-0302-7

• Articles • Previous Articles     Next Articles

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).

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

CLC Number: 

  • 60J65
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