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In this paper, we consider fractional parabolic equation of the form $ \frac{\partial u} {\partial t}=-(-\Delta )^{\frac{\alpha } {2}}u+u\dot W(t,x)$, where $-(-\Delta )^{\frac{\alpha } {2}}$ with $\alpha \in (0,2]$ is a fractional Laplacian and $\dot W$ is a Gaussian noise colored both in space and time. The precise moment Lyapunov exponents for the Stratonovich solution and the Skorohod solution are obtained by using a variational inequality and a Feynman-Kac type large deviation result for space-time Hamiltonians driven by $\alpha $-stable process. As a byproduct, we obtain the critical values for $\theta $ and $\eta $ such that $\mathbb{E} \exp \left (\theta \left (\int _0^1 \int _0^1 |r-s|^{-\beta _0}\gamma (X_r-X_s)drds\right )^\eta \right )$ is finite, where $X$ is $d$-dimensional symmetric $\alpha $-stable process and $\gamma (x)$ is $|x|^{-\beta }$ or $\prod _{j=1}^d|x_j|^{-\beta _j}$.

Pertenece a

Project Euclid (Hosted at Cornell University Library)  


Chen, Xia -  Hu, Yaozhong -  Song, Jian -  Song, Xiaoming - 

Id.: 71022954

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveLyapunov exponent - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 The Institute of Mathematical Statistics and the Bernoulli Society

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 1083-6489

Fecha de contribución: 16-mar-2018


* Electron. J. Probab.
* doi:10.1214/18-EJP139

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