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Uniqueness and explosion time of solutions of stochastic differential equations driven by fractional Brownian motion

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Abstract

In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion time in stochastic differential equations driven by fractional Browmian motion with respect to Hurst parameter more than half with small diffusion.

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Authors and Affiliations

  1. College of Mathematics, Sichuan University, Chengdu, 610064, P. R. China

    Jie Xu & Yun Min Zhu

  2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China

    Ji Cheng Liu

Authors
  1. Jie Xu
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  2. Yun Min Zhu
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  3. Ji Cheng Liu
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Correspondence to Yun Min Zhu.

Additional information

Supported in part by National Natural Science Foundation of China (Grant Nos. 10901065, 60934009)

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Xu, J., Zhu, Y.M. & Liu, J.C. Uniqueness and explosion time of solutions of stochastic differential equations driven by fractional Brownian motion. Acta. Math. Sin.-English Ser. 28, 2407–2416 (2012). https://doi.org/10.1007/s10114-012-1003-5

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  • DOI: https://doi.org/10.1007/s10114-012-1003-5

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