Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations

Weinan E; Arnulf Jentzen; Hao Shen

doi:10.1016/j.na.2016.03.001

Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations

Weinan E, Arnulf Jentzen, Hao Shen

Mathematics

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

11 Scopus citations

Abstract

This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and regularity of strong solutions of stochastic Ginzburg-Landau equations with polynomial nonlinearities in two space dimensions and with quadratic nonlinearities in three space dimensions.

Original language	English (US)
Pages (from-to)	152-193
Number of pages	42
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	142
DOIs	https://doi.org/10.1016/j.na.2016.03.001
State	Published - Sep 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

Renormalization
Stochastic Ginzburg-Landau equations

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10.1016/j.na.2016.03.001

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title = "Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations",

abstract = "This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and regularity of strong solutions of stochastic Ginzburg-Landau equations with polynomial nonlinearities in two space dimensions and with quadratic nonlinearities in three space dimensions.",

keywords = "Renormalization, Stochastic Ginzburg-Landau equations",

author = "Weinan E and Arnulf Jentzen and Hao Shen",

note = "Funding Information: The work of E and Shen is supported in part by grants from ARO ( W911NF-11-1-0101 ) and ONR ( N00014-01-1-0674 ). The work of Jentzen is supported in part by the research project “Numerical solutions of stochastic differential equations with non-globally Lipschitz continuous coefficients” funded by the German Research Foundation. Publisher Copyright: {\textcopyright} 2016 Elsevier Ltd.",

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T1 - Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations

AU - E, Weinan

AU - Jentzen, Arnulf

AU - Shen, Hao

N1 - Funding Information: The work of E and Shen is supported in part by grants from ARO ( W911NF-11-1-0101 ) and ONR ( N00014-01-1-0674 ). The work of Jentzen is supported in part by the research project “Numerical solutions of stochastic differential equations with non-globally Lipschitz continuous coefficients” funded by the German Research Foundation. Publisher Copyright: © 2016 Elsevier Ltd.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and regularity of strong solutions of stochastic Ginzburg-Landau equations with polynomial nonlinearities in two space dimensions and with quadratic nonlinearities in three space dimensions.

AB - This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and regularity of strong solutions of stochastic Ginzburg-Landau equations with polynomial nonlinearities in two space dimensions and with quadratic nonlinearities in three space dimensions.

KW - Renormalization

KW - Stochastic Ginzburg-Landau equations

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EP - 193

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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