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Density properties of the stochastic heat equations with degenerate conditions. Chen, Le
Description
In this talk, we study the stochastic heat equation on R^d driven by a multiplicative Gaussian noise which is white in time and colored in space. The diffusion coefficient rho can be degenerate, which includes the parabolic Anderson model rho(u)= u as a special case. The initial data is rough in the sense that it can be any measure, including the Dirac delta measure, that satisfies some mild integrability conditions. Under these degenerate conditions, for any given t>0 and distinct m points x_1, ... x_m in R^d, we establish the existence, regularity, and strict positivity of the joint density of the random vector (u(t,x_1), ...u(t,x_m)). The talk is based on a recent jointwork with Yaozhong Hu and David Nualart for the spatial dimension case, and an ongoing research project with Jingyu Huang for the higher spatial dimension case.
Item Metadata
Title |
Density properties of the stochastic heat equations with degenerate conditions.
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-09-13T11:32
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Description |
In this talk, we study the stochastic heat equation on R^d
driven by a multiplicative Gaussian noise which is white in time and
colored in space. The diffusion coefficient rho can be degenerate,
which includes the parabolic Anderson model rho(u)= u as a special
case. The initial data is rough in the sense that it can be any
measure, including the Dirac delta measure, that satisfies some mild
integrability conditions. Under these degenerate conditions, for any
given t>0 and distinct m points x_1, ... x_m in R^d, we establish the
existence, regularity, and strict positivity of the joint density of
the random vector (u(t,x_1), ...u(t,x_m)). The talk is based on a
recent jointwork with Yaozhong Hu and David Nualart for the spatial
dimension case, and an ongoing research project with Jingyu Huang for
the higher spatial dimension case.
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Extent |
28.0
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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 Nevada, Las Vegas
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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 |
10.14288/1.0377324
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Researcher
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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