带分数Brown运动和局部线性增长的随机微分方程

Abstract

Abstract:

In this paper, we discuss the existence and uniqueness of a class of stochastic differential equations driven by fractional Brown motion with Hurst parameter H ∈ ($\frac{1}{2}$, 1) and their coefficients are local linear growth. So far, there are several ways to define stochastic integrals with respect to FBM. In this paper, we define stochastic integrals with respect to FBM as a generalized Stieltjes integral. We give the existence and uniqueness theorems respectively for SDEs driven by fractional Brown motion and their coefficients are local linear growth.

Key words: Stochastic differential equations(SDE), Fractional Brownian motion, Generalized Stieltjes integral, Local linear growth, Adapted solution

CLC Number:

O211.63

Qikang Ran. SDE Driven by Fractional Brown Motion and Their Coefficients are Locally Linear Growth[J].Acta mathematica scientia,Series A, 2020, 40(1): 200-211.

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References 17

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SDE Driven by Fractional Brown Motion and Their Coefficients are Locally Linear Growth

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