Research article

Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients

  • Received: 23 December 2019 Accepted: 16 March 2020 Published: 14 April 2020
  • MSC : 60J27, 60H27, 60H28

  • In this paper, by using of the martingale property and positive maximum principle, we investigate the stochastic invariance for a class of hybrid stochastic differential equations (HSDEs) and provide necessary and sufficient conditions for the invariance of closed sets of $\mathbb{R}^d$ with non-Lipschitz coefficients. Moreover, an example of the most probable phase portrait is given to illustrate the effectiveness of the main results.

    Citation: Chunhong Li, Sanxing Liu. Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients[J]. AIMS Mathematics, 2020, 5(4): 3612-3633. doi: 10.3934/math.2020234

    Related Papers:

  • In this paper, by using of the martingale property and positive maximum principle, we investigate the stochastic invariance for a class of hybrid stochastic differential equations (HSDEs) and provide necessary and sufficient conditions for the invariance of closed sets of $\mathbb{R}^d$ with non-Lipschitz coefficients. Moreover, an example of the most probable phase portrait is given to illustrate the effectiveness of the main results.


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