Titlebook: Seminar on Stochastic Analysis, Random Fields and Applications IV; Centro Stefano Frans Robert C. Dalang,Marco Dozzi,Francesco Russo Confer

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Condition Numbers and Extrema of Random Fieldsds for the tails of the probability distribution of its . κ(.), defined as κ(.) = ∥A∥∥A.∥ when . is non-singular and κ(.)= + ∞ otherwise, where ∥∥ is Euclidean operator norm..An application is the obtention of inequality . where . is some known constant..The approach is based upon the so-called Rice

Deject

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Stochastic Heat and Burgers Equations and the Intermittence of Turbulencegive here a general theorem for Hamiltonian systems characterising how the level surfaces of Hamilton’s principal function (.) meet the caustic surface in both the deterministic and stochastic cases. We further show how these results can be applied to the stochastic Burgers equation. The generic exa

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Averaging of a Parabolic Partial Differential Equation with Random Evolutionefficients rapidly oscillating both in space and time variables. We extend to α < 2 and α > 2, the results by Pardoux and Piatnitski [.] (the case α = 2), and show that the structure of the limit problem depends crucially on α.

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Random Currents and Probabilistic Models of Vortex Filamentsollowing [.] and then we relate it to vortex filaments, in a new way with respect to [., ., .], but we also recall some facts from these works for comparison. Finally, we describe some attempts to define Gibbs measures on vortex lines. Related problems to random currents are:

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美学

Omnipotent

conscience

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