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

作　　者：Emenonye Christian Emenonye Donatus Anonwa Emenonye Christian Emenonye;Donatus Anonwa(Mathematics Department, University of Delta, Agbor, Nigeria;Mathematics Department, Delta State University, Abraka, Nigeria)

机构地区：[1]Mathematics Department, University of Delta, Agbor, Nigeria [2]Mathematics Department, Delta State University, Abraka, Nigeria

出　　处：《Applied Mathematics》2023年第3期196-207,共12页应用数学（英文）

摘　　要：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. .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. .

关 键 词：Approximate Solution Differential Equations Techniques Stochastic Differential Equation EXISTENCE UNIQUENESS Approximate Procedure 

分 类 号：O17[理学—数学]