Paper Title:

The Difference Between Two Approximate and Accurate Solutions of the Stochastic Differential Delay Equation Under Weak Conditions

Author(s):

Jin-Hyeong Kim and Young-Ho Kim

Department of Mathematics, Changwon National University,
Changwon, Gyeongsangnam 51140,
Korea.
E-mail: ginhyung5647@changwon.ac.kr
yhkim@changwon.ac.k

Abstract:

In this paper we investigates the existence of approximate solutions derived from the Caratheodory's and the Euler-Maruyama's scheme under a uniform Lipschitz condition and a weakened linear growth condition. And by analyzing the continuity and convergence of these approximate solutions, we would like to provide reliable results to approximate the unique solutions of stochastic functional differential delay equations. In particular, we investigate how quickly the approximate solution by the Carateodori and Euler-Maruyama approximation methods approaches the accurate solution of the equation.

Full Text PDF: