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作者：Mayer-Wolf, E.; Zakai, M.
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology
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作者：Csorgo, Miklos; Kulik, Rafal
作者单位：University of Sydney; Carleton University; University of Wroclaw
摘要：In this paper we consider quantile and Bahadur-Kiefer processes for long range dependent linear sequences. These processes, unlike in previous studies, are considered on the whole interval (0, 1). As it is well-known, quantile processes can have very erratic behavior on the tails. We overcome this problem by considering these processes with appropriate weight functions. In this way we conclude strong approximations that yield some remarkable phenomena that are not shared with i.i.d. sequences,...
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作者：Bryc, Wlodzimierz
作者单位：University System of Ohio; University of Cincinnati
摘要：We derive a non-asymptotic expression for the moments of traces of monomials in several independent complex Wishart matrices, extending some explicit formulas available in the literature. We then deduce the explicit expression for the cumulants. From the latter, we read out the multivariate normal approximation to the traces of finite families of polynomials in independent complex Wishart matrices.
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作者：Aidekon, Elie
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We consider a transient random walk (X-n) in random environment on a Galton-Watson tree. Under fairly general assumptions, we give a sharp and explicit criterion for the asymptotic speed to be positive. As a consequence, situations with zero speed are revealed to occur. In such cases, we prove that X-n is of order of magnitude n(Lambda), with Lambda is an element of (0, 1). We also show that the linearly edge reinforced random walk on a regular tree always has a positive asymptotic speed, whic...
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作者：Janvresse, Elise; Rittaud, Benoit; de la Rue, Thierry
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); Universite Paris 13
摘要：We study the random Fibonacci sequences defined by F-1 = F-2 = (F) over tilde (1) = (F) over tilde (2) = 1 and for n >= 1, Fn+2 = Fn+1 +/- F-n (linear case) and (F) over tilde (n+2) = vertical bar(F) over tilde (n+1) +/- (F) over tilde (n)vertical bar (non-linear case), where each +/- sign is independent and either + with probability p or - with probability 1 - p (0 < p <= 1). Our main result is that the exponential growth of F-n for 0 < p <= 1, and of F-n for 0 < p < <= 1, and of (F) over til...
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作者：Kargin, Vladislav
作者单位：New York University
摘要：This paper establishes necessary and sufficient conditions for the sequence of products of freely independent unitary operators to converge in distribution to the uniform law on the unit circle.
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作者：Janson, Svante; Neininger, Ralph
作者单位：Goethe University Frankfurt; Uppsala University
摘要：We consider the random fragmentation process introduced by Kolmogorov, where a particle having some mass is broken into pieces and the mass is distributed among the pieces at random in such a way that the proportions of the mass shared among different daughters are specified by some given probability distribution (the dislocation law); this is repeated recursively for all pieces. More precisely, we consider a version where the fragmentation stops when the mass of a fragment is below some given...
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作者：Goldsheid, Ilya Ya.
作者单位：University of London
摘要：The main goal of this work is to study the asymptotic behaviour of hitting times of a random walk (RW) in a quenched random environment (RE) on a strip. We introduce enlarged random environments in which the traditional hitting time can be presented as a sum of independent random variables whose distribution functions form a stationary random sequence. This allows us to obtain conditions (stated in terms of properties of random environments) for a linear growth of hitting times of relevant ran...
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作者：Watanabe, Toshiro
作者单位：University of Aizu
摘要：A serious gap in the Proof of Pakes's paper on the convolution equivalence of infinitely divisible distributions on the line is completely closed. It completes the real analytic approach to Sgibnev's theorem. Then the convolution equivalence of random sums of IID random variables is discussed. Some of the results are applied to random walks and Levy processes. In particular, results of Bertoin and Doney and of Korshunov on the distribution tail of the supremum of a random walk are improved. Fi...
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作者：Kleptsyna, M. L.; Veretennikov, A. Yu.
作者单位：University of Leeds; Le Mans Universite; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：For a class of non-uniformly ergodic Markov chains (X-n) satisfying exponential or polynomial beta-mixing, under observations (Y-n) subject to an IID noise with a positive density, it is shown that wrong initial data is forgotten in the mean total variation topology, with a certain exponential or polynomial rate.
