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Trotter-Kato approximations of stochastic neutral partial functional differential equations

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  • T. E. Govindan

    (National Polytechnic Institute)

Abstract

In this paper, a stochastic neutral partial functional differential equation is studied in real separable Hilbert spaces. The aim here is to introduce Trotter-Kato approximations of mild solutions for this class of equations. As an application, a classical limit theorem on the dependence of such equations on a parameter is obtained. Moreover, weak convergence of probability measures induced by the Trotter-Kato approximate mild solutions is established. An example is included at the end.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:3:d:10.1007_s13226-021-00146-0
    DOI: 10.1007/s13226-021-00146-0
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    References listed on IDEAS

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    1. 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.
    2. 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.
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