ON THE (STRICT) POSITIVITY OF SOLUTIONS OF THE STOCHASTIC HEAT EQUATION
成果类型：
Article
署名作者：
Moreno Flores, Gregorio R.
署名单位：
Pontificia Universidad Catolica de Chile
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/14-AOP911
发表日期：
2014
页码：
1635-1643
关键词：
摘要：
We give a new proof of the fact that the solutions of the stochastic heat equation, started with nonnegative initial conditions, are strictly positive at positive times. The proof uses concentration of measure arguments for discrete directed polymers in Gaussian environments, originated in M. Talagrand's work on spin glasses and brought to directed polymers by Ph. Carmona and Y. Hu. We also get slightly improved bounds on the lower tail of the solutions of the stochastic heat equation started with a delta initial condition.
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