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A NOTE ON THE APPROXIMATE SOLUTIONS TO STOCHASTIC DIFFERENTIAL DELAY EQUATION
A NOTE ON THE APPROXIMATE SOLUTIONS TO STOCHASTIC DIFFERENTIAL DELAY EQUATION
Journal of applied mathematics & informatics. 2016. Sep, 34(5_6): 421-434
  • Received : March 12, 2016
  • Published : September 30, 2016
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KIM, YOUNG-HO
PARK, CHAN-HO
BAE, MUN-JIN

Abstract
The main aim of this paper is to discuss the difference between the Euler-Maruyama's approximate solutions and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and weakened linear growth condition. Furthermore, we give the pth moment continuous of the approximate solution for the delay equation.
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