A note on almost sure asymptotic stability of neutral stochastic delay differential equations with Markovian switching

Authors:
Xiaoyue Li;Xuerong Mao
Affiliations:
School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, PR China;Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
Venue:
Automatica (Journal of IFAC)
Year:
2012

Citing 3
Cited 0

Numerical simulation and stability of stochastic systems with Markovian switching

Neural, Parallel & Scientific Computations
On Strong Feller, Recurrence, and Weak Stabilization of Regime-Switching Diffusions

SIAM Journal on Control and Optimization
Some New Aspects of Lyapunov-Type Theorems for Stochastic Differential Equations of Neutral Type

SIAM Journal on Control and Optimization

Quantified Score

Hi-index	22.14

Visualization

Abstract

In this paper, we consider neutral stochastic delay differential equations with Markovian switching. Our key aim is to establish LaSalle-type stability theorems for the underlying equations. The key techniques used in this paper are the method of Lyapunov functions and the convergence theorem of nonnegative semi-martingales. The key advantage of our new results lies in the fact that our results can be applied to more general non-autonomous equations.