Titlebook: Stochastic Space—Time Models and Limit Theorems; L. Arnold,P. Kotelenez Book 1985 D. Reidel Publishing Company, Dordrecht, Holland 1985 Ma

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Markov Processes on Infinite Dimensional Spaces, Markov Fields and Markov Cosurfacesruction of homogeneous generalized Markov random fields. We also discuss a non commutative extension to the case where the state space is a group. The extension involves a stochastic calculus for group valued mappings defined on hypersurfaces of codimension 1.

带来墨水

Stochastic Integration of Banach Space Valued Functionsation theory is the L.-isometry between the space of square integrable predictable functions X (relative to the Doléans measure of M.) and the space of the stochastic integrals ∫XdM. This result extends without major difficulties to the case that M is Hilbert space valued and X belongs to a suitable space of operator-valued predictable functions.

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内阁

A Central Limit Theorem for a System of Interacting Particles denote by X(j,t) the number of particles at site j at time t, let ρ be its expectation. The corresponding . are the S’-valued processes N., defined by . (S’: space of Schwartz distributions on R., S: space of rapidly decaying smooth functions).

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On the Semigroup Approach to Stochastic Evolution EquationsThis paper deals with properties of mild solutions of stochastic partial differential equations (with and without delays). Both the case of a fixed Hilbert state space and the case of a nuclear Gel’ fand triple as state space are analyzed. Examples of parabolic and hyperbolic equations are given.

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作茧自缚

Tightness Of Sequences Of Hilbert Valued MartingalesThis paper gives a sufficient condition for the tightness of a sequence (M.). of Hubert valued martingales. This result applies directly to some situations of “accompanying martingales” as considered for example by L. Arnold, M. Theodosopulu and P. Kotelenez.

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Asymptotic Analysis of a Semi-Linear PDE with Wide-Band Noise DisturbancesWe present an asymptotic analysis in the “white-noise limit” of a semi-linear parabolic partial differential equation, whose coefficients are perturbed by a wide-band noise. We prove the convergence in law towards the solution of an Ito stochastic PDE, thus generalizing the results in [3] for linear PDEs.

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