Abstract
In this paper, the exponential stability of stochastic differential equations driven by multiplicative fractional Brownian motion (fBm) with Markovian switching is investigated. The quasi-linear cases with the Hurst parameter H ∈ (1/2, 1) and linear cases with H ∈ (0, 1/2) and H ∈ (1/2, 1) are all studied in this work. An example is presented as a demonstration.
Highlights
In the natural world, it is a common phenomena that many practical systems may face random abrupt changes in their structures and parameters, such as environmental variance, changing of subsystem interconnections and so on
Much attention has been paid to the stability of stochastic hybrid systems
Mao [4] considers the exponential stability of general nonlinear stochastic hybrid systems
Summary
It is a common phenomena that many practical systems may face random abrupt changes in their structures and parameters, such as environmental variance, changing of subsystem interconnections and so on. Mao [4] considers the exponential stability of general nonlinear stochastic hybrid systems. In [5], the criteria of moment exponential stability are obtained for stochastic hybrid delayed systems with Lévy noise in mean square. Equation 1 can be regarded as the result of the following N fractional stochastic differential equations: dXt f(Xt, t, i)dt + g(Xt, t, i)dBHt , 1 ≤ i ≤ N, X0 x0 > 0, switching from one to another according to the movement of {rt}t ≥ 0.
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