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

  • Etsuo Isobe (a1) and Shunsuke Sato (a1)
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.

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∗∗ Postal address: Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, 560 Japan.
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∗)

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

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References
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Doob, J. L. (1953) Stochastic Processes. Wiley, New York.
Hida, T. (1980) Brownian Motion. Springer-Verlag, Berlin.
Itô, K. (1951) Multiple Wiener integral J. Math. Soc. Japan 3, 157169.
Marmarelis, P. Z. and Marmarelis, V. Z. (1978) Analysis of Physiological Systems. Plenum Press, New York.
Mckean, H. P. (1969) Stochastic Integrals. Academic Press, New York.
Nishio, M. (1961) Remark on the canonical representation of strictly stationary processes. J. Math. Kyoto Univ. 1, 129146.
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.
Wiener, N. (1958) Nonlinear Problems in Random Theory. MIT Press, Cambridge, Mass.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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