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Wiener–Hermite expansion of a process generated by an Itô stochastic differential equation

Published online by Cambridge University Press:  14 July 2016

Etsuo Isobe
Affiliation:
Osaka University
Shunsuke Sato
Affiliation:
Osaka University

Abstract

In this paper we deal with the Wiener–Hermite expansion of a process generated by an Itô stochastic differential equation. The so-called Wiener kernels which appear in the functional series expansion are expressed in terms of the transition probability density function of the process.

Keywords

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

∗)

Present address: Mitsubishi Research Institute, Inc., Ootemachi, Chiyoda-ku, Tokyo 100, Japan.

References

Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google ScholarPubMed
Hida, T. (1980) Brownian Motion. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Itô, K. (1951) Multiple Wiener integral J. Math. Soc. Japan 3, 157169.CrossRefGoogle Scholar
Marmarelis, P. Z. and Marmarelis, V. Z. (1978) Analysis of Physiological Systems. Plenum Press, New York.CrossRefGoogle Scholar
Mckean, H. P. (1969) Stochastic Integrals. Academic Press, New York.Google Scholar
Nishio, M. (1961) Remark on the canonical representation of strictly stationary processes. J. Math. Kyoto Univ. 1, 129146.CrossRefGoogle Scholar
Siegel, A., Imamura, T. and Meecham, W. C. (1965) Wiener–Hermite expansion in model turbulence in the late decay state. J. Math. Phys. 6, 707721.CrossRefGoogle Scholar
Wiener, N. (1958) Nonlinear Problems in Random Theory. MIT Press, Cambridge, Mass.Google Scholar
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