Some analytic approximations for neutral stochastic functional differential equations |
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Authors: | Svetlana Jankovi? Maja Vasilova |
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Institution: | Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia |
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Abstract: | We consider an analytic iterative method to approximate the solution of a neutral stochastic functional differential equation. More precisely, we define a sequence of approximate equations and we give sufficient conditions under which the approximate solutions converge with probability one and in pth moment sense, p ? 2, to the solution of the initial equation. We introduce the notion of the Z-algorithm for this iterative method and present some examples to illustrate the theory. Especially, we point out that the well-known Picard method of iterations is a special Z-algorithm. |
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Keywords: | Neutral stochastic functional differential equation Z-algorithm approximate solutions Convergence with probability one and in pth mean |
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