Continuous Disintegrations of Gaussian Processes

Preprint English OPEN
LaGatta, Tom;
(2010)
  • Subject: 41A65, 47A50 | Mathematics - Probability | Mathematics - Functional Analysis

The goal of this paper is to understand the conditional law of a stochastic process once it has been observed over an interval. To make this precise, we introduce the notion of a continuous disintegration: a regular conditional probability measure which varies continuou... View more
  • References (16)
    16 references, page 1 of 2

    [1] D.R. Bell. The Malliavin Calculus. Longman Scientific and Technical, 1987.

    [2] L. Bergamaschi. Geostatistics in hydrology: Kriging interpolation. http://www.dmsa.unipd.it/~berga/Teaching/STAM/stat.pdf.

    [3] A. Berlinet and C. Thomas-Agnan. Reproducing kernel Hilbert spaces in probability and statistics. Kluwer Academic Publishers, 2004.

    [4] P. Billingsley. Convergence of probability measures, volume 2333096. Wiley New York, 1968.

    [5] V.I. Bogachev. Measure Theory Vol. I-II, 2007.

    [6] J.T. Chang and D. Pollard. Conditioning as disintegration. Statistica Neerlandica, 51(3):287-317, 1997.

    [7] R. Durrett. Probability: theory and examples. Duxbury Press Belmont, CA, 1996.

    [8] GB Folland. Real Analysis: Modern Techniques and Their Applications. Wiley-Interscience, 1999.

    [9] L. Gross. Abstract Wiener spaces. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probablility, volume 2, 1964.

    [10] S. Janson. Gaussian Hilbert Spaces. Cambridge University Press, 1997.

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