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2019 Can the stochastic wave equation with strong drift hit zero?
Kevin Lin, Carl Mueller
Electron. J. Probab. 24: 1-26 (2019). DOI: 10.1214/19-EJP279

Abstract

We study the stochastic wave equation with multiplicative noise and singular drift:

\[\partial _{t}u(t,x)=\Delta u(t,x)+u^{-\alpha }(t,x)+g(u(t,x))\dot{W} (t,x)\]

where $x$ lies in the circle $\mathbf{R} /J\mathbf{Z} $ and $u(0,x)>0$. We show that

(i) If $0<\alpha <1$ then with positive probability, $u(t,x)=0$ for some $(t,x)$.

(ii) If $\alpha >3$ then with probability one, $u(t,x)\ne 0$ for all $(t,x)$.

Citation

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Kevin Lin. Carl Mueller. "Can the stochastic wave equation with strong drift hit zero?." Electron. J. Probab. 24 1 - 26, 2019. https://doi.org/10.1214/19-EJP279

Information

Received: 26 February 2018; Accepted: 11 February 2019; Published: 2019
First available in Project Euclid: 20 February 2019

zbMATH: 1412.60092
MathSciNet: MR3916334
Digital Object Identifier: 10.1214/19-EJP279

Subjects:
Primary: 60H15
Secondary: 35L05, 60J45

JOURNAL ARTICLE
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