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A semilinear Mckean-Vlasov stochastic evolution equation in Hilbert space

Author

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  • Ahmed, N. U.
  • Ding, X.

Abstract

This paper deals with a semilinear stochastic equation in a real Hilbert space and formulates a related McKean-Vlasov type measure-valued evolution equation. It is shown that the stochastic equation has a unique mild solution such that the corresponding probability law is the unique measure-valued solution of McKean-Vlasov evolution equation.

Suggested Citation

  • Ahmed, N. U. & Ding, X., 1995. "A semilinear Mckean-Vlasov stochastic evolution equation in Hilbert space," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 65-85, November.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:1:p:65-85
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    Cited by:

    1. Lu, Wen & Ren, Yong & Hu, Lanying, 2015. "Mean-field backward stochastic differential equations in general probability spaces," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 1-11.
    2. Liu, Huoxia & Lin, Judy Yangjun, 2023. "Stochastic McKean–Vlasov equations with Lévy noise: Existence, attractiveness and stability," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Govindan, T.E., 2015. "On Trotter–Kato approximations of semilinear stochastic evolution equations in infinite dimensions," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 299-306.
    4. Li, Zhi & Luo, Jiaowan, 2012. "Mean-field reflected backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1961-1968.
    5. T. E. Govindan, 2021. "Trotter-Kato approximations of stochastic neutral partial functional differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(3), pages 822-836, September.
    6. Govindan, T.E., 2014. "Weak convergence of probability measures of Yosida approximate mild solutions of neutral SPDEs," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 26-32.
    7. Lu, Wen & Ren, Yong & Hu, Lanying, 2015. "Mean-field backward stochastic differential equations with subdifferential operator and its applications," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 73-81.

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