### Abstract

Language | English |
---|---|

Pages | 1-24 |

Number of pages | 24 |

Journal | Annals of Probability |

Publication status | Accepted/In press - 19 Sep 2014 |

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### Keywords

- intermittence
- stochastic partial differential equations

### Cite this

*Annals of Probability*, 1-24.

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*Annals of Probability*, pp. 1-24.

**Moment bounds for a class of fractional stochastic heat equations.** / Foondun, Mohammud; Liu, Wei; Omaba, McSylvester.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Moment bounds for a class of fractional stochastic heat equations

AU - Foondun, Mohammud

AU - Liu, Wei

AU - Omaba, McSylvester

PY - 2014/9/19

Y1 - 2014/9/19

N2 - We consider fractional stochastic heat equations of the form $\frac{\partial u_t(x)}{\partial t} = -(-\Delta)^{\alpha/2} u_t(x)+\lambda \sigma (u_t(x)) \dot F(t,\, x)$. Here $\dot F$ denotes the noise term. Under suitable assumptions, we show that the second moment of the solution grows exponentially with time. In particular, this answers an open problem in \cite{CoKh}. Along the way, we prove a number of other interesting properties which extend and complement results in \cite{foonjose}, \cite{Khoshnevisan:2013aa} and \cite{Khoshnevisan:2013ab}.

AB - We consider fractional stochastic heat equations of the form $\frac{\partial u_t(x)}{\partial t} = -(-\Delta)^{\alpha/2} u_t(x)+\lambda \sigma (u_t(x)) \dot F(t,\, x)$. Here $\dot F$ denotes the noise term. Under suitable assumptions, we show that the second moment of the solution grows exponentially with time. In particular, this answers an open problem in \cite{CoKh}. Along the way, we prove a number of other interesting properties which extend and complement results in \cite{foonjose}, \cite{Khoshnevisan:2013aa} and \cite{Khoshnevisan:2013ab}.

KW - intermittence

KW - stochastic partial differential equations

M3 - Article

SP - 1

EP - 24

JO - Annals of Probability

T2 - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

ER -