The monotonicity inequality for linear stochastic partial differential equations

Leszek Gawarecki; Vidyadhar Mandrekar; Bhaskaran Rajeev

doi:10.1142/S0219025709003902

The monotonicity inequality for linear stochastic partial differential equations

Leszek Gawarecki, Vidyadhar Mandrekar, Bhaskaran Rajeev

Kettering University

Michigan State University

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

Abstract

We prove the monotonicity inequality for differential operators A and L that occur as coefficients in linear stochastic partial differential equations associated with finite-dimensional Itô processes. We characterize the solutions of such equations. A probabilistic representation is obtained for solutions to a class of evolution equations associated with time dependent, possibly degenerate, second-order elliptic differential operators.

Original language	American English
Journal	Infinite Dimensional Analysis Quantum Probability and Related Topics
Volume	12
DOIs	https://doi.org/10.1142/S0219025709003902
State	Published - Aug 2 2006

Keywords

Finite-dimensional and infinite-dimensional stochastic partial differential equations
multi-Hilbertian spaces
nuclear spaces
existence
uniqueness
coercivity
monotonicity
probabilistic representations
evolution equations

Disciplines

Mathematics

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10.1142/S0219025709003902License: CC BY

https://www.worldscientific.com/doi/pdf/10.1142/S0219025709003902

Cite this

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title = "The monotonicity inequality for linear stochastic partial differential equations",

abstract = " We prove the monotonicity inequality for differential operators A and L that occur as coefficients in linear stochastic partial differential equations associated with finite-dimensional It{\^o} processes. We characterize the solutions of such equations. A probabilistic representation is obtained for solutions to a class of evolution equations associated with time dependent, possibly degenerate, second-order elliptic differential operators.",

keywords = "Finite-dimensional and infinite-dimensional stochastic partial differential equations, multi-Hilbertian spaces, nuclear spaces, existence, uniqueness, coercivity, monotonicity, probabilistic representations, evolution equations",

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AU - Gawarecki, Leszek

AU - Mandrekar, Vidyadhar

AU - Rajeev, Bhaskaran

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N2 - We prove the monotonicity inequality for differential operators A and L that occur as coefficients in linear stochastic partial differential equations associated with finite-dimensional Itô processes. We characterize the solutions of such equations. A probabilistic representation is obtained for solutions to a class of evolution equations associated with time dependent, possibly degenerate, second-order elliptic differential operators.

AB - We prove the monotonicity inequality for differential operators A and L that occur as coefficients in linear stochastic partial differential equations associated with finite-dimensional Itô processes. We characterize the solutions of such equations. A probabilistic representation is obtained for solutions to a class of evolution equations associated with time dependent, possibly degenerate, second-order elliptic differential operators.

KW - Finite-dimensional and infinite-dimensional stochastic partial differential equations

KW - multi-Hilbertian spaces

KW - nuclear spaces

KW - existence

KW - uniqueness

KW - coercivity

KW - monotonicity

KW - probabilistic representations

KW - evolution equations

UR - https://digitalcommons.kettering.edu/mathematics_facultypubs/2

UR - https://www.worldscientific.com/doi/pdf/10.1142/S0219025709003902

U2 - 10.1142/S0219025709003902

DO - 10.1142/S0219025709003902

M3 - Article

VL - 12

JO - Infinite Dimensional Analysis Quantum Probability and Related Topics

JF - Infinite Dimensional Analysis Quantum Probability and Related Topics

ER -

The monotonicity inequality for linear stochastic partial differential equations

Abstract

Keywords

Disciplines

Access to Document

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