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Existence and uniqueness of stochastic differential equations with random impulses and Markovian switching under non-lipschitz conditions

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Abstract

In the paper, stochastic differential equations with random impulses and Markovian switching are brought forward, where the so-called random impulse means that impulse ranges are driven by a series of random variables and impulse times are a random sequence, so these equations extend stochastic differential equations with jumps and Markovian switching. Then the existence and uniqueness of solutions to such equations are investigated by employing the Bihari inequality under non-Lipschtiz conditions.

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Authors and Affiliations

  1. School of Finance and Statistics, East China Normal University, Shanghai, 200241, P. R. China

    Shu Jin Wu & Bin Zhou

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  1. Shu Jin Wu
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  2. Bin Zhou
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Correspondence to Shu Jin Wu.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 10771070), Doctoral Program Foundation of Ministry of Education of China (Grant No. 20060269016), and Natural Science Foundation of Shanghai (Grant No. 08ZR1407000)

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Wu, S.J., Zhou, B. Existence and uniqueness of stochastic differential equations with random impulses and Markovian switching under non-lipschitz conditions. Acta. Math. Sin.-English Ser. 27, 519–536 (2011). https://doi.org/10.1007/s10114-011-9753-z

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  • DOI: https://doi.org/10.1007/s10114-011-9753-z

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