Carathéodory’s approximate solution to stochastic differential delay equation

Kim, Young‐Ho

doi:10.2298/fil1607019k

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Furthermore, equations from this class have unique solutions with bounded moments and their coefficients satisfy polynomial conditions. [4] considered the stochastic differential equation and defined the Caratheodory's approximate solution of stochastic differential delay equation.…”

Section: Related Literaturementioning

confidence: 99%

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

Emenonye¹,

Anonwa²

2023

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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.

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Section: Related Literaturementioning

confidence: 99%

“…To make the theory more understandable, we impose the non-uniform Lipschitz condition and non-linear growth condition. The Euler method discretisation has an optimal strong convergence rate and [5] established Caratheodory's and Euler approximate solutions to stochastic differential delay equation.…”

Section: Related Literaturementioning

confidence: 99%

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

Emenonye¹,

Anonwa²

2023

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“…By using the nonlinear growth condition and nonlinear growth condition, in 2015, Kim [4] studied the difference between the approximate solution and the accurate solution to the stochastic differential delay equation (shortly, SDEs).…”

Section: Introductionmentioning

confidence: 99%

Caratheodory's approximate solution to stochastic differential delay equation

Cho¹,

Kim²

2017

J. Nonlinear Sci. Appl.

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Existence and uniqueness theorem of solution for stochastic differential equations driven by G-Brownian motion

Hacène,

Amar

2024

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Due to the different applications of the stochstic differential equations in many areas of life, such as physics, mechanical and electrical engineering, as well as economic and finance. Many researchers have been interested in studying these equations, as they have proven in many cases that they accept unique solutions, as well as their stability in some cases according to various conditions, especially Lypschitz conditions and growth conditions with different methods. Many physical phenomena and economic and financial issues have been modeled using these equations. These studies have witnessed rapid developments recently, as some researchers have expanded them to sublinear spaces by replacing Brownian motion with G-Brownian motion and setting more precise conditions to reach very important results. In this paper we prove the existence and the uniqueness of solution for a stochastic differential equation driven by G-Brownian motion where the coefficients of the equation satisfy the weakened Hölder condition and a weakened linear growth condition.

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Carathéodory’s approximate solution to stochastic differential delay equation

Abstract: The main aim of this paper is to discuss Carathéodory's and Euler-Maruyama's approximate solutions to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and non-linear growth condition.

Cited by 3 publications

References 9 publications

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

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

Caratheodory's approximate solution to stochastic differential delay equation

Existence and uniqueness theorem of solution for stochastic differential equations driven by G-Brownian motion

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