Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN ESTIMATE OF THE SOLUTIONS FOR STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Kim, Young-Ho (Department of Mathematics, Changwon National University)
  • Received : 2011.02.09
  • Accepted : 2011.03.18
  • Published : 2011.09.30
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Abstract

In this paper, we give an estimate on the difference between $x^n(t)$ and x(t) and it clearly shows that one can use the Picard iteration procedure to the approximate solutions to stochastic functional differential equations with infinite delay at phase space BC(($-{\infty}$, 0] : $R^d$) which denotes the family of bounded continuous $R^d$-valued functions ${\varphi}$ defined on ($-{\infty}$, 0] with norm ${\parallel}{\varphi}{\parallel}={\sup}_{-{\infty}<{\theta}{\leq}0}{\mid}{\varphi}({\theta}){\mid}$ under non-Lipschitz condition being considered as a special case and a weakened linear growth condition.

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References

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