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On Simulating Wiener Integrals and Their Expectations

Published online by Cambridge University Press:  27 July 2009

A. Korzeniowski  and
D.L. Hawkins
A. Korzeniowski
Affiliation:
Department of Mathematics University of Texas at Arlington, Arlington, Texas 76019
D.L. Hawkins
Affiliation:
Department of Mathematics University of Texas at Arlington, Arlington, Texas 76019
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Abstract

An approximation scheme for evaluating Wiener integrals by simulating Brownian motion is studied. The rate of convergence and numerical results are given, including an application to the heat equation by using the Feynman-Kac formula.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 1 , January 1991 , pp. 101 - 112
Copyright
Copyright © Cambridge University Press 1991

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References

Chorin, A.J. (1973). Accurate evaluation of Wiener integrals. Mathematics of Computation 27: 1–15.CrossRefGoogle Scholar
Bilingsley, P. (1968). Convergence of probability measures. New York: Wiley.Google Scholar
Blankenship, G.L. & Baras, J.S. (1981). Accurate evaluation of stochastic Wiener integrals with applications to scattering in random media and to nonlinear filtering. SIAM Journal of Applied Mathematics 41: 518–552.CrossRefGoogle Scholar
Borisov, I.S. (1980). On conditions of existence of bounded density for additive functionals on some random processes. Theory of Processes and Its Applications 25: 454–465.CrossRefGoogle Scholar
Borovkov, A.A. (1973). On the rate of convergence for the invariance principle. Theory of Probability and Its Applications 18: 207–225.CrossRefGoogle Scholar
Feinsilver, P. (1978). Lecture notes in mathematics, #696. New York: Springer-Verlag.Google Scholar
Haeusler, E. (1984). An exact rate of convergence in the functional central limit theorem for special martingale difference arrays. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte 65: 523–534.CrossRefGoogle Scholar
Korzeniowski, A. (1985). Dynamic systems driven by Markov processes. Journal of Mathematical Physics 26: 2189–2191.CrossRefGoogle Scholar
Milshtejn, G.N. (1985). Weak approximation of solutions of systems of stochastic differential equations. Theory of Probability and Its Applications 30: 750–766.Google Scholar
Pardoux, E. & Talay, D. (1985). Discretization and simulation of stochastic differential equations. Acta Applicauolae Mathematicae 3: 23–47.CrossRefGoogle Scholar
Ripley, B.D. (1987). Stochastic simulation. New York: Wiley.CrossRefGoogle Scholar
Shoenfelder, C. & Cambanis, S. (1982). Random designs for estimating integrals of stochastic processes. Annals of Mathematical Statistics 10: 526–538.Google Scholar
Wagner, W. (1987). Unbiased Monte Carlo evaluation of certain functional integrals. Journal of Computational Physics 71: 21–33.CrossRefGoogle Scholar