Stability of stochastic differential equation with linear fractal noise

doi:10.1007/s11464-014-0355-9

Front. Math. China

2014, Vol. 9

Issue (3) : 495-507 https://doi.org/10.1007/s11464-014-0355-9

RESEARCH ARTICLE

Stability of stochastic differential equation with linear fractal noise

Junjun LIAO,Xiangjun WANG(

)

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

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Abstract

We study a class of stochastic differential equation with linear fractal noise. By an auxiliary stochastic differential equation, we prove the existence and uniqueness of the solution under some mild assumptions. We also give some estimates of moments of the solution. The exponential stability of the solution is discussed.

Keywords Fractional Brownian motion (FBM) stochastic differential equation (SDE) exponential p-stability λ-exponential p-stability

Issue Date: 24 June 2014

Cite this article:

Junjun LIAO,Xiangjun WANG. Stability of stochastic differential equation with linear fractal noise[J]. Front. Math. China, 2014, 9(3): 495-507.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0355-9
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I3/495

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