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July 2014 On the (strict) positivity of solutions of the stochastic heat equation
Gregorio R. Moreno Flores
Ann. Probab. 42(4): 1635-1643 (July 2014). DOI: 10.1214/14-AOP911

Abstract

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.

Citation

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Gregorio R. Moreno Flores. "On the (strict) positivity of solutions of the stochastic heat equation." Ann. Probab. 42 (4) 1635 - 1643, July 2014. https://doi.org/10.1214/14-AOP911

Information

Published: July 2014
First available in Project Euclid: 3 July 2014

zbMATH: 1306.60088
MathSciNet: MR3262487
Digital Object Identifier: 10.1214/14-AOP911

Subjects:
Primary: 60H15, 60K35, 60K37

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 4 • July 2014
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