Small Kappa Asymptotics of the Almost Sure Lyapunov Exponent for the Continuum Parabolic Anderson Model

Michael Rael

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arXiv · 1209.2993

Small Kappa Asymptotics of the Almost Sure Lyapunov Exponent for the Continuum Parabolic Anderson Model

Michael Rael

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Abstract

We prove that the almost sure Lyapunov exponent \lambda(\kappa) of the continuous space Parabolic Anderson Model is bounded above by $c_u \kappa^{1/3}$ as $\kappa\downarrow0$ under mild regularity conditions. This bound of the same order of the previously proven lower bound, $\lambda(\kappa) \ge c_l \kappa^{1/3}$.

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Michael Rael. 2012-09-13. Small Kappa Asymptotics of the Almost Sure Lyapunov Exponent for the Continuum Parabolic Anderson Model. https://arxiv.org/abs/1209.2993

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