Asymptotics for the almost sure lyapunov exponent for the solution of the parabolic Anderson problem

Rene A. Carmona; Leonid Koralov; Stanislav Molchanov

doi:10.1515/rose.2001.9.1.77

Asymptotics for the almost sure lyapunov exponent for the solution of the parabolic Anderson problem

Rene A. Carmona
, Leonid Koralov
, Stanislav Molchanov

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We consider the Stochastic Partial Differential Equation [equation presented] The potential is assumed to be Gaussian white noise in time, stationary in space. We obtain the asymptotics of the almost sure Lyapunov exponent γ(k) for the solution as k→0. Namely γ(k)∼c0/ln(1/ k), where the constant C0 is determined by the correlation function of the potential.

Original language	English (US)
Pages (from-to)	77-86
Number of pages	10
Journal	Random Operators and Stochastic Equations
Volume	9
Issue number	1
DOIs	https://doi.org/10.1515/rose.2001.9.1.77
State	Published - Jan 2001

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability

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10.1515/rose.2001.9.1.77

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title = "Asymptotics for the almost sure lyapunov exponent for the solution of the parabolic Anderson problem",

abstract = "We consider the Stochastic Partial Differential Equation [equation presented] The potential is assumed to be Gaussian white noise in time, stationary in space. We obtain the asymptotics of the almost sure Lyapunov exponent γ(k) for the solution as k→0. Namely γ(k)∼c0/ln(1/ k), where the constant C0 is determined by the correlation function of the potential.",

author = "Carmona, \{Rene A.\} and Leonid Koralov and Stanislav Molchanov",

year = "2001",

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AU - Koralov, Leonid

AU - Molchanov, Stanislav

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Y1 - 2001/1

N2 - We consider the Stochastic Partial Differential Equation [equation presented] The potential is assumed to be Gaussian white noise in time, stationary in space. We obtain the asymptotics of the almost sure Lyapunov exponent γ(k) for the solution as k→0. Namely γ(k)∼c0/ln(1/ k), where the constant C0 is determined by the correlation function of the potential.

AB - We consider the Stochastic Partial Differential Equation [equation presented] The potential is assumed to be Gaussian white noise in time, stationary in space. We obtain the asymptotics of the almost sure Lyapunov exponent γ(k) for the solution as k→0. Namely γ(k)∼c0/ln(1/ k), where the constant C0 is determined by the correlation function of the potential.

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DO - 10.1515/rose.2001.9.1.77

M3 - Article

AN - SCOPUS:21644441966

SN - 0926-6364

VL - 9

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EP - 86

JO - Random Operators and Stochastic Equations

JF - Random Operators and Stochastic Equations

IS - 1

ER -

Asymptotics for the almost sure lyapunov exponent for the solution of the parabolic Anderson problem

Abstract

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