TY - JOUR
T1 - Asymptotics for the almost sure lyapunov exponent for the solution of the parabolic Anderson problem
AU - Carmona, Rene A.
AU - Koralov, Leonid
AU - Molchanov, Stanislav
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2001/1
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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U2 - 10.1515/rose.2001.9.1.77
DO - 10.1515/rose.2001.9.1.77
M3 - Article
AN - SCOPUS:21644441966
SN - 0926-6364
VL - 9
SP - 77
EP - 86
JO - Random Operators and Stochastic Equations
JF - Random Operators and Stochastic Equations
IS - 1
ER -