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Kim, Y.H. (2015) The Difference between the Approximate and the Accurate Solution to Stochastic Differential Delay Equation. Proceedings of the Jangjeon Mathematical Society, 18, 165-175.

has been cited by the following article:

• TITLE: A Comparative Survey of an Approximate Solution Method for Stochastic Delay Differential Equations

  AUTHORS: Emenonye Christian Emenonye, Donatus Anonwa

  KEYWORDS: Approximate Solution, Differential Equations, Techniques, Stochastic Differential Equation, Existence, Uniqueness, Approximate Procedure

  JOURNAL NAME: Applied Mathematics, Vol.14 No.3, March 28, 2023

  ABSTRACT: This study is focused on the approximate solution for the class of stochastic delay differential equations. The techniques applied involve the use of Caratheodory and Euler Maruyama procedures which approximated to stochastic delay differential equations. Based on the Caratheodory approximate procedure, it was proved that stochastic delay differential equations have unique solution and established that the Caratheodory approximate solution converges to the unique solution of stochastic delay differential equations under the Cauchy sequence and initial condition. This Caratheodory approximate procedure and Euler method both converge at the same rate. This is achieved by replacing the present state with past state. The existence and uniqueness of an approximate solution of the stochastic delay differential equation were shown and the approximate solution to the unique solution was also shown.