The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

A Caratheodory's Approximate Solutions of Stochastic Differential Equations Under the Hölder Condition


Bo-Kyeong Kim and Young-Ho Kim

Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnam-do 51140,


In this paper, based on the theorem of the uniqueness of the solution of the stochastic differential equation, the convergence possibility of the Caratheodory's approximate solution was studied by approximating the unique solution. To obtain this convergence theorem, we used a Hölder condition and a weakened linear growth condition. Furthermore, The auxiliary theorems for the existence and continuity of the Caratheodory's approximate solution were investigated as a prerequisite.

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