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Second order Lyapunov exponent for hyperbolic Anderson model Balan, Raluca
Description
In this talk, we examine the connection between the hyperbolic and parabolic Anderson models in arbitrary space dimension d, with constant initial condition, driven by a Gaussian noise which is white in time. We consider two spatial covariance structures: (i) the Fourier transform of the spectral measure of the noise is a non-negative locally-integrable function; (ii) d = 1 and the noise is a fractional Brownian motion in space with index 1/4 < H < 1/2. In both cases, we show that there is striking similarity between the Laplace transforms of the second moment of the solutions to these two models. Building on this connection and the recent powerful results of Huang, Le and Nualart (2017) for the parabolic model, we compute the second order (upper) Lyapunov exponent for the hyperbolic model. In case (i), when the spatial covariance of the noise is given by the Riesz kernel, we present a unified method for calculating the second order Lyapunov exponents for the two models.
Item Metadata
Title |
Second order Lyapunov exponent for hyperbolic Anderson model
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-09-12T10:02
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Description |
In this talk, we examine the connection between the hyperbolic and
parabolic Anderson models in arbitrary space dimension d, with constant
initial condition, driven by a Gaussian noise which is white in time. We
consider two spatial covariance structures: (i) the Fourier transform of the
spectral measure of the noise is a non-negative locally-integrable function; (ii)
d = 1 and the noise is a fractional Brownian motion in space with index 1/4 <
H < 1/2. In both cases, we show that there is striking similarity between
the Laplace transforms of the second moment of the solutions to these two
models. Building on this connection and the recent powerful results of Huang,
Le and Nualart (2017) for the parabolic model, we compute the second order
(upper) Lyapunov exponent for the hyperbolic model. In case (i), when the
spatial covariance of the noise is given by the Riesz kernel, we present a
unified method for calculating the second order Lyapunov exponents for the
two models.
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Extent |
27.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Ottawa
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Series | |
Date Available |
2019-03-22
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0377321
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International