Article
The monotonicity inequality for linear stochastic partial differential equations
Infinite Dimensional Analysis Quantum Probability and Related Topics
Document Type
Article
Publication Date
8-2-2006
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.
Disciplines
DOI
10.1142/S0219025709003902
Rights
© 2018 World Scientific Publishing Co Pte Ltd
Citation Information
Leszek Gawarecki, Vidyadhar Mandrekar and Bhaskaran Rajeev. "The monotonicity inequality for linear stochastic partial differential equations" Infinite Dimensional Analysis Quantum Probability and Related Topics Vol. 12 Iss. 4 (2006) p. 1 - 19 ISSN: Print ISSN: 0219-0257 Online ISSN: 1793-6306 Available at: http://works.bepress.com/leszek-gawarecki/12/