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Multidimensional statistics, especially in the case where the sample size and the number of estimated parameters (or hypotheses tested) are comparable, is a natural area of application of the theory of random matrices (see V. L. Girko, Statistical Analysis of Observations of Increasing Dimension...
We present a new class of polynomials that are solutions of the generalized Laplace differential equation, written in spherical coordinates. Differentiation properties, orthogonality, Rodrigues like formula, recurrence relations, generating functions and an integral representation are discussed....
We consider a general linear stochastic wave equation driven by fractional-in-time noise. We solve the equation and study its energy. We find asymptotic results for the expected energy for large and small times and as the Hurst parameter, H approaches 1/2. Finally we use analytic continuation to...
Let Ñ t be a standard compensated Poisson process on 0, 1. We prove a new characterization of anticipating integrals of the Skorokhod type with respect to Ñ , and use it to obtain several counterparts to well established properties of semimartingale stochastic integrals. In particular we show...
Our main result is an infinitesimal characterization of Hilbert module module flows, not necessarily of inner type, in terms of stochastic derivations from the initial algebra into the Itô algebra. We prove that any such derivation is the difference of a *-homomorphism and the trivial embedding.
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