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作者：Deheuvels, P
作者单位：Sorbonne Universite
摘要：The notion of a kth iterated Kiefer process K(nu, t; k) for k is an element of N and nu, t is an element of R is introduced. We show that the uniform quantile process beta (n)(t) may be approximated on [0, 1] by n(-1/2) K(n, t; k), at an optimal uniform almost sure rate of O(n(-1/2+1/2k+1+0(1))) for each k is an element of N. Our arguments are based in part on a new functional limit law, of independent interest, for the increments of the empirical process; Applications include an extended vers...
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作者：Maxwell, M; Woodroofe, M
作者单位：California State University System; San Jose State University; University of Michigan System; University of Michigan
摘要：Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say S-n = g(X-1) + ... + g(X-n), where E[g(X-1)] = 0 and E[g(X-1)(2)] < . The conditions imposed restrict the moments of g and the growth of the conditional means E(S-n\X-1). No other restrictions on the dependence structure of the chain are required. When specialized to shift processes, the conditions are implied by simple integral tests involving g.
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作者：Erickson, KB
作者单位：University of Washington; University of Washington Seattle
摘要：Given any closed subset C of (R-d)overbar, containing a pair of antipodal points at oo, there is a sequence of independent and identically distributed random variables {X-i} such that the set of limit points (in the topology of (R-d)overbar) of {(X-1 +...+X-t)/t}(t greater than or equal to 1) equals C. Here (R-d) is the compact space gotten by adjoining the sphere, S(d-1)infinity at infinity.
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作者：Virág, B
作者单位：University of California System; University of California Berkeley
摘要：Lyons, Pemantle and Peres asked whether the asymptotic lower speed in an infinite tree is bounded by the asymptotic speed in the regular tree with the same average number of branches. In the more general setting of random walks on graphs, we establish a bound on the expected value of the exit time from a vertex set in terms of the size and distance from the origin of its boundary, and prove this conjecture. We give sharp bounds for limiting speed (or, when applicable, sublinear rate of escape)...
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作者：Arratia, R; Barbour, AD; Tavaré, S
作者单位：University of Southern California; University of Zurich
摘要：Under very mild conditions, we prove that the limiting behavior of the component counts in a decomposable logarithmic combinatorial structure conforms to a single, unified pattern, which includes functional central limit theorems, Erdas-Turan laws, Poisson-Dirichlet limits for the large components and Poisson approximation in total variation for the total number of components. Our approach is entirely probabilistic, and the conditions can readily be verified in practice.
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作者：Ben Arous, G; Ramírez, AF
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Pontificia Universidad Catolica de Chile
摘要：We consider a model of diffusion in random media with a two-way coupling (i.e., a model in which the randomness of the medium influences the diffusing particles and where the diffusing particles change the medium). In this particular model, particles are injected at the origin with a time-dependent rate and diffuse among random traps. Each trap has a finite (random) depth, so that when it has absorbed a finite (random) number of particles it is saturated, and it no longer acts as a trap. This ...
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作者：Cranston, M; Wang, FY
作者单位：University of Rochester; Beijing Normal University
摘要：It is proved in this paper that a weak parabolic Harnack inequality for a Markov semigroup implies the existence of a coupling and a shift coupling for the corresponding process with equal chances of success. This implies equality of the tail and invariant sigma -fields for the diffusion as well as equality of the class of bounded parabolic functions and the class of bounded harmonic functions.
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作者：Jacod, J; Méléard, S; Protter, P
作者单位：Sorbonne Universite; Universite Paris Nanterre; Purdue University System; Purdue University
摘要：Stochastic integral representation of martingales has been undergoing a renaissance due to questions motivated by stochastic finance theory. In the Brownian case one usually has formulas (of differing degrees of exactness) for the predictable integrands. We extend some of these to Markov cases where one does not necessarily have stochastic integral representation of all martingales. Moreover we study various convergence questions that arise naturally from (for example) approximations of price ...
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作者：Cerf, R; Pisztora, A
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Carnegie Mellon University
摘要：We study the phase separation phenomenon ilo the Ising model in dimensions d greater than or equal to 3. To this end we work in a large box with plus boundary conditions and we condition the system to have an excess amount of negative spins so that the empirical magnetization is smaller than the spontaneous magnetization m*. We confirm the prediction of the phenomenological theory by proving that with high probability a single droplet of the minus phase emerges surrounded by the plus phase. Mo...
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作者：Deheuvels, P; Einmahl, JH
作者单位：Sorbonne Universite; Eindhoven University of Technology
摘要：We prove functional limit laws for the increment functions of empirical processes based upon randomly right-censored data. The increment sizes we consider are classified into different classes covering the whole possible spectrum. We apply these results to obtain a description of the strong limiting behavior of a series of estimators of local functionals of lifetime distributions. In particular, we treat the case of kernel density and hazard rate estimators.
