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Global existence of solutions for stochastic impulsive differential equations

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Abstract

In this paper we obtain some results on the global existence of solution to Itô stochastic impulsive differential equations in M([0,∞),ℝn) which denotes the family of ℝn-valued stochastic processes x satisfying supt∈[0,∞) \( \mathbb{E} \)|x(t)|2 < ∞ under non-Lipschitz coefficients. The Schaefer fixed point theorem is employed to achieve the desired result. An example is provided to illustrate the obtained results.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, 200092, P. R. China

    Li Juan Shen & Ji Tao Sun

  2. Department of Mathematics, Luoyang Normal University, Luoyang, 471022, P. R. China

    Li Juan Shen

Authors
  1. Li Juan Shen
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  2. Ji Tao Sun
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Corresponding author

Correspondence to Ji Tao Sun.

Additional information

Supported by NSF of the Department of Education, He’nan Province (Grant No. 2008B110010), the Development Programs in Science and Technology of He’nan Province (Grant No. 092300410187), NSF of China (Grant No. 60874027)

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Shen, L.J., Sun, J.T. Global existence of solutions for stochastic impulsive differential equations. Acta. Math. Sin.-English Ser. 27, 773–780 (2011). https://doi.org/10.1007/s10114-011-8650-9

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  • DOI: https://doi.org/10.1007/s10114-011-8650-9

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