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作者：RIO, E
摘要：Let (X(i))(i is an element of Z) be a strictly stationary and strongly mixing sequence of real-valued mean zero random variables. Let (alpha(n))(n>0) be the sequence of strong mixing coefficients. We define the strong mixing fraction alpha (.) by alpha(t) = alpha([t]) and we denote by Q the quantile function of \X(0)\. Assume that (*) integral(0)(1) alpha(-1)(t)Q(2)(t)dt < infinity, where f(-1) denotes the inverse of the monotonic function f. The main result of this paper is that the functiona...
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作者：HSING, TL
摘要：It is shown that Sigma(i=1)(n) X(n) and max(i=1)(n)X(i) are asymptotically independent if {X(i)} is strongly mixing and Sigma(i=1)(n)X(i) is asymptotically Gaussian. This generalizes a result of Anderson and Turkman.
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作者：REINERT, G
作者单位：University of Zurich
摘要：Let E be a locally compact Hausdorff space with countable basis and let (X(i))(i epsilon N) be a family of random elements on E with (1/n) Sigma(i=1)(n) L (X(i)) double right arrow(>)v mu(n --> infinity) for a measure mu with parallel to mu parallel to less than or equal to 1. Conditions are derived under which L ((1/n) Sigma(i=1)(n) (delta)X(i)) double right arrow(w) delta(mu)(n --> infinity), where delta(x), denotes the Dirac measure at x. The proof being based on Stein's method, there are g...
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作者：ROSINSKI, J
摘要：A connection between structural studies of stationary non-Gaussian stable processes and the ergodic theory of nonsingular flows is established and exploited. Using this connection, a unique decomposition of a stationary stable process into three independent stationary parts is obtained. It is shown that the dissipative part of a flow generates a mixed moving average part of a stationary stable process, while the identity part of a flow essentially gives the harmonizable part. The third part of...
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作者：Stong, R
摘要：This paper gives sharp bounds on the eigenvalues of a natural random walk on the group of upper triangular n x n matrices over the field of characteristic p, an odd prime, with 1's on the diagonal. In particular, this includes the finite Heisenberg groups as a special case. As a consequence we get bounds on the time required to achieve randomness for these walks. Some of the steps are done using the geometric bounds on the eigenvalues of Diaconis and Stroock. However, the crucial step is done ...
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作者：DJEHICHE, B; KAJ, I
作者单位：Uppsala University
摘要：A principle of large deviations from the McKean-Vlasov Limit is derived for a class of measure-valued jump processes. It is shown that the associated rate function admits several representations, including the one obtained by entropy methods and the one derived by a pathwise approach.
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作者：ADLER, RJ; SAMORODNITSKY, G
作者单位：Cornell University
摘要：We consider the full weak convergence, in appropriate function spaces, of systems of noninteracting particles undergoing critical branching and following a self-similar spatial motion with stationary increments. The limit processes are measure-valued, and are of the super and historical process type. In the case in which the underlying motion is that of a fractional Brownian motion, we obtain a characterization of the limit process as a kind of stochastic integral against the historical proces...
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作者：SIMONELLI, I
摘要：Let S be a countable set and Lambda the collection of all subsets of S. We consider interacting particle systems (IPS) {eta(t)} on Lambda, with duals {<(eta)over tilde>(t)}, and duality equation P[\eta(t)(xi)boolean AND A\ odd] = (P) over tilde[\<(eta)over tilde>(A)(t) A boolean AND xi\ odd], xi, A subset of S, A finite. Under certain conditions we find all the extreme invariant distributions that arise as limits of translation invariant initial configurations. Specific systems will be conside...
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作者：VERZANI, J
摘要：A slow point from the left for Brownian motion is a time during a given interval for which the oscillations of the path immediately to the left of this time are smaller than the typical ones, that is, those given by the local LIL. These slow points occur at random times during a given interval. For historical super-Brownian motion, the support at a fixed time contains an infinite collection of paths. This paper makes use of a branching process description of the support to investigate the slow...
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作者：Newman, CM; Piza, MST
