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Numerical Analysis of Explicit One-Step Methods for Stochastic Delay Differential Equations

  • Christopher T. H. Baker (a1) and Evelyn Buckwar (a2)
Abstract
Abstract

We consider the problem of strong approximations of the solution of stochastic differential equations of Itô form with a constant lag in the argument. We indicate the nature of the equations of interest, and give a convergence proof in full detail for explicit one-step methods. We provide some illustrative numerical examples, using the Euler–Maruyama scheme.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

9.R. D. Driver , Ordinary and delay differential equations, Appl. Math. Sci. 20 (Springer, New York, 1977).

16.V. Kolmanovskiĭ and A. Myshkis , Applied theory of functional-differential equations (Kluwer Academic Publishers Group, Dordrecht, 1992).

21.G. N. Milstein , Numerical integration of stochastic differential equations (translated and revised from the 1988 Russian original) (Kluwer, Dordrecht, 1995).

27.D. Talay , ‘Simulation of stochastic differential systems’, Probabilistic methods in applied physics, Lecture Notes in Phys. 451 (ed. P. Kree and W. Wedig , Springer, Berlin, 1995) 5496.

29. D. Williams , Probability with martingales (Cambridge University Press, Cambridge, 1991).

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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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