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On large deviations in Hilbert space

Published online by Cambridge University Press:  20 January 2009

Nigel J. Cutland
Affiliation:
Department of Pure MathematicsUniversity of HullHU6 7RX, England
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Abstract

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Nonstandard methods and a flat integral representation are used to give a simple and intuitive proof of the large deviation principle for a Gaussian measure on a separable Hilbert space.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

REFERENCES

1.Albeverio, S., Fenstad, J. E., Høegh-Krohn, R. and Lindstrom, T., Nonstandard Methods in Stochastic Analysis and Mathematical Physics (Academic Press, New York 1986).Google Scholar
2.Cutland, N. J., Infinitesimals in action, J. London Math. Soc. 35 (1987), 202216.CrossRefGoogle Scholar
3.Cutland, N. J., An action functional for Lévy Brownian motion, Acta Appl. Math. 18 (1990), 261281.CrossRefGoogle Scholar
4.Cutland, N. J. (Editor), Nonstandard Analysis and its Applications (Cambridge University Press, 1988).CrossRefGoogle Scholar
5.Kurd, A. E. and Loeb, P. A., An Introduction to Nonstandard Real Analysis (Academic Press, New York, 1985).Google Scholar
6.Kuo, H.-H., Gaussian Measures in Banach Spaces (Lecture Notes in Mathematics, Vol. 463, Spinger-Verlag, Berlin, 1975).CrossRefGoogle Scholar
7.Stroock, D. W., An Introduction to the Theory of Large Deviations (Springer-Verlag, New York, 1984).CrossRefGoogle Scholar