NitroFlare A Dirichlet Problem for Distributions and Specifications for Random Fields

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    A Dirichlet Problem for Distributions and Specifications for Random Fields (Memoirs of the American Mathematical Society) by Michael Rockner
    English | 15 Dec. 1985 | ISBN: 0821823256 | 76 Pages | PDF | 5 MB

    We explicitly construct consistent conditional distributions for a large class of Gaussian measures defined on the space of (tempered) distributions on a domain D in IR . The conditional distributions are with respect to an (uncountable) family of o-fields associated with the complements of the (relatively compact) open subsets of D.

    The construction involves solving a Dirichlet problem whose "boundary data" is given by a distribution. Furthermore, the associated set of Gibbs states is studied. We characterize the extreme Gibbs states, prove that they have the global Markov property and, using the Dirichlet solution for distributions, we can represent any Gibbs state in terms of extreme Gibbs states.[​IMG]
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