• Title/Summary/Keyword: Neutral stochastic functional differential equation

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MOMENT ESTIMATE AND EXISTENCE FOR THE SOLUTION OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION

  • Chen, Huabin;Wan, Qunjia
    • Journal of the Korean Mathematical Society
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    • v.59 no.2
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    • pp.279-298
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    • 2022
  • In this paper, the existence and uniqueness for the global solution of neutral stochastic functional differential equation is investigated under the locally Lipschitz condition and the contractive condition. The implicit iterative methodology and the Lyapunov-Razumikhin theorem are used. The stability analysis for such equations is also applied. One numerical example is provided to illustrate the effectiveness of the theoretical results obtained.

AN EXISTENCE OF THE SOLUTION TO NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS UNDER SPECIAL CONDITIONS

  • KIM, YOUNG-HO
    • Journal of applied mathematics & informatics
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    • v.37 no.1_2
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    • pp.53-63
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    • 2019
  • In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.