Abstract
Abstract The aim of this work is to study the asymptotic stability of the time-changed stochastic delay differential equations (SDDEs) with Markovian switching. Some sufficient conditions for the asymptotic stability of solutions to the time-changed SDDEs are presented. In contrast to the asymptotic stability in existing articles, we present the new results on the stability of solutions to time-changed SDDEs, which is driven by time-changed Brownian motion. Finally, an example is given to demonstrate the effectiveness of the main results.
Highlights
The research on stochastic differential equations (SDEs) plays an important role in modeling dynamic system areas, such as physics, economics and finance, biological and so forth
It is well known that time delay is unavoidable in practice, the corresponding stochastic delay differential equations (SDDEs) are used more widely in systems
In [19], we considered the exponential stability for the time-changed stochastic functional differential equations with Markov switching
Summary
The research on stochastic differential equations (SDEs) plays an important role in modeling dynamic system areas, such as physics, economics and finance, biological and so forth. It is well known that time delay is unavoidable in practice, the corresponding stochastic delay differential equations (SDDEs) are used more widely in systems. It considers the effects of past behaviors imposed to the current status. In [19], we considered the exponential stability for the time-changed stochastic functional differential equations with Markov switching. Motivated strongly by the above, in this paper, we will study the stability of time-changed SDDEs with Markovian switching. An example is given to illustrate the effectiveness of the main results
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