Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 3: 495 - 507

DOI: https://doi.org/10.1007/s11464-014-0355-9

RESEARCH ARTICLE

Stability of stochastic differential equation with linear fractal noise

  • Junjun LIAO ,
  • Xiangjun WANG
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  • School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Received date: 26 Jul 2013

Accepted date: 23 Dec 2013

Published date: 24 Jun 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Fractional Brownian motion (FBM); stochastic differential equation (SDE); exponential p-stability; λ-exponential p-stability

Cite this article

Junjun LIAO , Xiangjun WANG . Stability of stochastic differential equation with linear fractal noise[J]. Frontiers of Mathematics in China, 2014 , 9(3) : 495 -507 . DOI: 10.1007/s11464-014-0355-9

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