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December 1, 2013
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October 24, 2013
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Abstract. We construct intrinsic on- and off-diagonal upper and lower estimates for the transition probability density of a Lévy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of the process. The technique used in the paper relies on the asymptotic analysis of the inverse Fourier transform of the respective characteristic function. We provide several examples, in particular, with rather irregular Lévy measure, to illustrate our results.
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November 12, 2013
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Abstract. We consider the Wigner ensemble of Hermitian n -dimensional random matrices with elements and study the asymptotic behavior of the expression in the limit such that and are the values of the order . Assuming that the random variables have a symmetric probability distribution such that all of its moments are of the sub-gaussian form, we prove that the limit of exists and does not depend on the particular values of , . The proof is based on a combination of the arguments by Ya. Sinai and A. Soshnikov with the detailed study of a moment analog of the Green's function representation of the Inverse Participation Ratio (IPR) considered for Gaussian Unitary Invariant Ensemble of random matrices (GUE).
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October 25, 2013
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Abstract. Several scientific and technical problems can be described by a stochastic partial differential equation. The solution of the equation could be considered as the limit of a suitable discrete particle model. The existence of such a kind of approximation was discussed in [Serdica 13 (1987), 396–402]. In this paper we will consider a completely discrete particle model.
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November 5, 2013
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Abstract. In the paper we consider the distributions of random variables represented by the alternating Lüroth series (-expansion). We study Lebesgue structure, topological, metric and fractal properties of these random variables. We prove that random variable with independent -symbols has a pure discrete, pure absolutely continuous or pure singularly continuous distribution. We describe topological and metric properties of the spectra of distributions of random variables as well as properties of their probability distribution functions.
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November 2, 2013
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Abstract. We study the estimation of parameters of one-dimensional diffusion processes that are discretely observed. We construct an estimator of the parameters based on the minimum Hellinger distance method. Under conditions which ensure the ergodicity and geometrically α-mixing of the Markov process, we establish the almost sure convergence and the asymptotic normality of the estimator.