• Title/Summary/Keyword: neutral stochastic differential equations

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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.

DIFFERENTIABILITY OF NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY G-BROWNIAN MOTION WITH RESPECT TO THE INITIAL DATA

  • Zakaria Boumezbeur;Hacene Boutabia
    • Honam Mathematical Journal
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    • v.45 no.3
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    • pp.433-456
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    • 2023
  • This paper deals with differentiability of solutions of neutral stochastic differential equations with respect to the initial data in the G-framework. Since the initial data belongs to the space BC ([-r, 0] ; ℝn) of bounded continuous ℝn-valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space 𝓛BC (ℝn) of linear bounded operators from BC ([-r, 0] ; ℝn) to ℝn. We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.

EXISTENCE UNIQUENESS AND STABILITY OF NONLOCAL NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH RANDOM IMPULSES AND POISSON JUMPS

  • CHALISHAJAR, DIMPLEKUMAR;RAMKUMAR, K.;RAVIKUMAR, K.;COX, EOFF
    • Journal of Applied and Pure Mathematics
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    • v.4 no.3_4
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    • pp.107-122
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    • 2022
  • This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we demonstrate the stability via continuous dependence initial value. Our study extends the work of Wang, and Wu [16] where the time delay is addressed by the prescribed phase space 𝓑 (defined in Section 3). To illustrate the theory, we also provide an example of our methods. Using our results, one could investigate the controllability of random impulsive neutral stochastic differential equations with finite/infinite states. Moreover, one could extend this study to analyze the controllability of fractional-order of NRINSDEs with Poisson jumps as well.

EXISTENCE, UNIQUENESS AND STABILITY OF IMPULSIVE STOCHASTIC PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

  • Anguraj, A.;Vinodkumar, A.
    • Journal of applied mathematics & informatics
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    • v.28 no.3_4
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    • pp.739-751
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    • 2010
  • This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation.

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.

EXISTENCE AND STABILITY RESULTS FOR STOCHASTIC FRACTIONAL NEUTRAL DIFFERENTIAL EQUATIONS WITH GAUSSIAN NOISE AND LÉVY NOISE

  • P. Umamaheswari;K. Balachandran;N. Annapoorani;Daewook Kim
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.2
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    • pp.365-382
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    • 2023
  • In this paper we prove the existence and uniqueness of solution of stochastic fractional neutral differential equations with Gaussian noise or Lévy noise by using the Picard-Lindelöf successive approximation scheme. Further stability results of nonlinear stochastic fractional dynamical system with Gaussian and Lévy noises are established. Examples are provided to illustrate the theoretical results.