Stability of stochastic differential equation with linear fractal noise

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

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Higher Education Press and Springer-Verlag Berlin Heidelberg