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作者：Basdevant, Anne-Laure; Schapira, Bruno; Singh, Arvind
作者单位：Universite Paris Nanterre; Universite Paris Saclay; Universite Paris Saclay
摘要：We characterize nondecreasing weight functions for which the associated one-dimensional vertex reinforced random walk (VRRW) localizes on 4 sites. A phase transition appears for weights of order n log log n: for weights growing faster than this rate, the VRRW localizes almost surely on, at most, 4 sites, whereas for weights growing slower, the VRRW cannot localize on less than 5 sites. When w is of order n log log n, the VRRW localizes almost surely on either 4 or 5 sites, both events happenin...
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作者：Cuny, Christophe; Merlevede, Florence
作者单位：Universite Paris Saclay; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in H (a real and separable Hilbert space) admits an approximation, in L-p (H), p > 1, by a martingale with stationary differences, and we then estimate the error of approximation in L-p (H). The results are exploited to further investigate the behavior of the partial sums. In particular we obtain new projective conditions concerning the Marcinkiewicz-Z...
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作者：Kifer, Yuri; Varadhan, S. R. S.
作者单位：Hebrew University of Jerusalem; New York University
摘要：We obtain functional central limit theorems for both discrete time expressions of the form 1/root N Sigma([Nt])(n=1) (F(X(q(1)(n)),...,X(q(l)(n))) - (F) over bar) and similar expressions in the continuous time where the sum is replaced by an integral. Here X(n), n >= 0 is a sufficiently fast mixing vector process with some moment conditions and stationarity properties, F is a continuous function with polynomial growth and certain regularity properties, (F) over bar = integral F d(mu X ... X mu...
