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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
KIM, YOUNG-HO;PARK, CHAN-HO;BAE, MUN-JIN
Journal of applied mathematics & informatics. 2016. Sep, 34(5_6): 421-434
DOI : http://dx.doi.org/10.14317/jami.2016.421
  • Received : March 12, 2016
  • Published : September 30, 2016
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KIM, YOUNG-HO
PARK, CHAN-HO
BAE, MUN-JIN
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KIM, YOUNG-HO
PARK, CHAN-HO
BAE, MUN-JIN
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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.
Keywords
Euler-Maruyama approximation ;  non-Lipschitz condition ;  weakened linear growth condition ;  Stochastic differential delay equation
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Citing 'A NOTE ON THE APPROXIMATE SOLUTIONS TO STOCHASTIC DIFFERENTIAL DELAY EQUATION '
@article{ E1MCA9_2016_v34n5_6_421} ,title={A NOTE ON THE APPROXIMATE SOLUTIONS TO STOCHASTIC DIFFERENTIAL DELAY EQUATION} ,volume={5_6} , url={http://dx.doi.org/10.14317/jami}, DOI={10.14317/jami} , number= {5_6} , journal={Journal of applied mathematics & informatics} , publisher={Korean Society of Computational and Applied Mathematics} , author={YOUNG-HO, KIM and CHAN-HO, PARK and MUN-JIN, BAE} , year={2016} , month={Sep}