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Order preservation for multidimensional stochastic functional differential equations with jumps

Order preservation for multidimensional stochastic functional differential equations with jumps Sufficient and necessary conditions are presented for the order preservation of stochastic functional differential equations on $${\mathbb{R}^d}$$ R d with non-Lipschitzian coefficients driven by the Brownian motion and Poisson processes. The sufficiency of the conditions extends and improves some known comparison theorems derived recently for one-dimensional equations and multidimensional equations without delay, and the necessity is new even in these special situations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Order preservation for multidimensional stochastic functional differential equations with jumps

Journal of Evolution Equations , Volume 14 (2) – Jun 1, 2014

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References (17)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer Basel
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-014-0222-x
Publisher site
See Article on Publisher Site

Abstract

Sufficient and necessary conditions are presented for the order preservation of stochastic functional differential equations on $${\mathbb{R}^d}$$ R d with non-Lipschitzian coefficients driven by the Brownian motion and Poisson processes. The sufficiency of the conditions extends and improves some known comparison theorems derived recently for one-dimensional equations and multidimensional equations without delay, and the necessity is new even in these special situations.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Jun 1, 2014

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