Stochastic partial differential equations with unbounded and degenerate coefficients

Xicheng Zhang

doi:10.1016/j.jde.2010.11.021

Stochastic partial differential equations with unbounded and degenerate coefficients

Xicheng Zhang^*

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

In this article, using DiPerna-Lions theory (DiPerna and Lions, 1989) [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L¹-integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinear filtering problem and also obtain the existence and uniqueness of generalized solutions for a degenerate nonlinear SPDE.

Original language	English
Pages (from-to)	1924-1966
Number of pages	43
Journal	Journal of Differential Equations
Volume	250
Issue number	4
DOIs	https://doi.org/10.1016/j.jde.2010.11.021
Publication status	Published - 15 Feb 2011
Externally published	Yes

Keywords

DiPerna-Lions theory
Maximal principle
Nonlinear filtering
Stochastic partial differential equation

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10.1016/j.jde.2010.11.021

Cite this

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title = "Stochastic partial differential equations with unbounded and degenerate coefficients",

abstract = "In this article, using DiPerna-Lions theory (DiPerna and Lions, 1989) [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1-integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinear filtering problem and also obtain the existence and uniqueness of generalized solutions for a degenerate nonlinear SPDE.",

keywords = "DiPerna-Lions theory, Maximal principle, Nonlinear filtering, Stochastic partial differential equation",

author = "Xicheng Zhang",

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AU - Zhang, Xicheng

PY - 2011/2/15

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N2 - In this article, using DiPerna-Lions theory (DiPerna and Lions, 1989) [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1-integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinear filtering problem and also obtain the existence and uniqueness of generalized solutions for a degenerate nonlinear SPDE.

AB - In this article, using DiPerna-Lions theory (DiPerna and Lions, 1989) [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1-integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinear filtering problem and also obtain the existence and uniqueness of generalized solutions for a degenerate nonlinear SPDE.

KW - DiPerna-Lions theory

KW - Maximal principle

KW - Nonlinear filtering

KW - Stochastic partial differential equation

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DO - 10.1016/j.jde.2010.11.021

M3 - Article

AN - SCOPUS:78650989143

SN - 0022-0396

VL - 250

SP - 1924

EP - 1966

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -

Stochastic partial differential equations with unbounded and degenerate coefficients

Abstract

Keywords

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