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New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients

Author

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  • Lan, Guangqiang
  • Wu, Jiang-Lun

Abstract

The objective of the present paper is to find new sufficient conditions for the existence of unique strong solutions to a class of (time-inhomogeneous) stochastic differential equations with random, non-Lipschitzian coefficients. We give an example to show that our conditions are indeed weaker than those relevant conditions existing in the literature. We also derive moment estimations for the maximum process of the solution. Finally, we present a sufficient condition to ensure the non confluence property of the solution of time-homogeneous SDE which, in one dimension, is nothing but stochastic monotone property of the solution.

Suggested Citation

  • Lan, Guangqiang & Wu, Jiang-Lun, 2014. "New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4030-4049.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:4030-4049
    DOI: 10.1016/j.spa.2014.07.010
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    Cited by:

    1. Xu, Jie & Wen, Jiaping & Mu, Jianyong & Liu, Jicheng, 2019. "Stochastic flows of SDEs with non-Lipschitz coefficients and singular time," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 118-127.
    2. Lan, Guangqiang & Xia, Fang & Zhao, Mei, 2020. "pth moment (p∈(0,1)) and almost sure exponential stability of the exact solutions and modified truncated EM method for stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 160(C).
    3. Junxia Duan & Jun Peng, 2022. "An Approximation Scheme for Reflected Stochastic Differential Equations with Non-Lipschitzian Coefficients," Journal of Theoretical Probability, Springer, vol. 35(1), pages 575-602, March.

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