Stochastic invariance for neutral functional differential equation with non-lipschitz coefficients

Chunhong Li; Jiaowan Luo

doi:10.3934/dcdsb.2018321

Article Contents

2019, Volume 24, Issue 7: 3299-3318. Doi: 10.3934/dcdsb.2018321

This issue Previous Article On a beam model related to flight structures with nonlocal energy damping Next Article On the global convergence of frequency synchronization for Kuramoto and Winfree oscillators

Stochastic invariance for neutral functional differential equation with non-lipschitz coefficients

Chunhong Li^1, and
Jiaowan Luo^1, ,

Department of Probability and Statistics, School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, MO 510006, China

^* Corresponding author: Jiaowan Luo
^* Corresponding author: Jiaowan Luo

Received: January 31, 2018

Revised: June 30, 2018

Early access: January 2019

Published: May 2019

The second author is supported by NNSF grant 11271093.

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Abstract

In this paper, by the use of martingale property and spectral decomposition theory, we investigate the stochastic invariance for neutral stochastic functional differential equations (NSFDEs) and provide necessary and sufficient conditions for the invariance of closed sets of $ R^{d} $ with non-Lipschitz coefficients. A pathwise asymptotic estimate example is given to illustrate the feasibility and effectiveness of obtained result.

Keywords:

Linear growth condition,
local martingale,
neutral stochastic functional differential equation,
stochastic invariance,
spectral decomposition.

Mathematics Subject Classification: Primary: 60H30, 60H25; Secondary: 65C30.

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