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Title	Density properties of the stochastic heat equations with degenerate conditions.
Creator	Chen, Le
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-09-13T11:32
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.
Extent	28.0
Subject	Mathematics Probability theory and stochastic processes Partial differential equations
Geographic Location	Oaxaca (Mexico : State)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: University of Nevada, Las Vegas
Series	BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))
Date Available	2019-03-22
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0377324
URI	http://hdl.handle.net/2429/69084
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Researcher
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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