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Introduction and Motivating Examples

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Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications

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Abstract

Stochastic differential equations, in the sense of Itô, arise quite naturally as mathematical models in many areas of science, engineering and finance. Problems such as existence and uniqueness of mild solutions; stability and optimal control; continuous dependence on initial values; Yosida and Trotter-Kato approximations, among others, of mild solutions of stochastic differential equations in infinite-dimensional spaces have been investigated by many authors, see Ahmed [1, 2], Bharucha-Reid [1], Curtain and Pritchard [1], Da Prato [1], Da Prato and Zabczyk [1, 3, 4], Gawarecki and Mandrekar [1], Govindan [13], Itô [2], Kallianpur and **ong [1], Kotelenez [1], Liu [1], Liu and Röckner [1], Lototsky and Rozovsky [1], Mandrekar and Rüdiger [1], McKibben [2], Métivier [2], Peszat and Zabczyk [1] and Prévôt and Röckner [1], to mention only a few, and the references cited therein.

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Authors and Affiliations

  1. National Polytechnic Institute, Mexico City, Mexico

    T. E. Govindan

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  1. T. E. Govindan
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Correspondence to T. E. Govindan .

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Govindan, T.E. (2024). Introduction and Motivating Examples. In: Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications. Springer, Cham. https://doi.org/10.1007/978-3-031-42791-6_1

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