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作者：Benjamini, I; Häggström, O; Peres, Y; Steif, JE
作者单位：University of Gothenburg; University of California System; University of California Berkeley; Hebrew University of Jerusalem; University System of Georgia; Georgia Institute of Technology; Chalmers University of Technology
摘要：Consider a sequence of i.i.d. random variables, where each variable is refreshed (i.e., replaced by an independent variable with the same law) independently, according to a Poisson clock. At any fixed time t, the resulting sequence has the same law as at time 0, but there can be exceptional random times at which certain almost sure properties of the time 0 sequence are violated. We prove that there are no such exceptional times for the law of large numbers and the law of the iterated logarithm...
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作者：Klüppelberg, C; Pergamenchtchikov, S
作者单位：Technical University of Munich; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Motivated by multivariate random recurrence equations we prove a new analogue of the Key Renewal Theorem for functionals of a Markov chain with compact state space in the spirit of Kesten [Ann. Probab. 2 (1974) 355-386]. Compactness of the state space and a certain continuity condition allows us to simplify Kesten's proof considerably.
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作者：Arnaudon, M; Thalmaier, A
作者单位：Universite de Poitiers; University of Bonn
摘要：We characterize Yang-Mills connections in vector bundles in terms of covariant derivatives of stochastic parallel transport along variations of Brownian bridges on the base manifold. In particular, we prove that a connection in a vector bundle E is Yang-Mills if and only if the covariant derivative of parallel transport along Brownian bridges (in the direction of their drift) is a local martingale, when transported back to the starting point. We present a Taylor expansion up to order 3 for sto...
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作者：Choirat, C; Hess, C; Seri, R
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：In this paper, we prove a new version of the Birkhoff ergodic theorem (BET) for random variables depending on a parameter (alias integrands). This involves variational convergences, namely epigraphical, hypographical and uniform convergence and requires a suitable definition of the conditional expectation of integrands. We also have to establish the measurability of the epigraphical lower and upper limits with respect to the or-field of invariant subsets. From the main result, applications to ...
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作者：Reitzner, M
作者单位：Technische Universitat Wien; University of Freiburg
摘要：Let K be a smooth convex body. The convex hull of independent random points in K is a random polytope. Estimates for the variance of the volume and the variance of the number of vertices of a random polytope are obtained. The essential step is the use of the Efron-Stein jackknife inequality for the variance of symmetric statistics. Consequences are strong laws of large numbers for the volume and the number of vertices of the random polytope. A conjecture of Barany concerning random and best-ap...
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作者：Pitt, LD; Robeva, RS
作者单位：University of Virginia
摘要：Let Phi = {phi(x):x is an element of R-2} be a Gaussian random field on the plane. For A subset of R-2, we investigate the relationship between the sigma-field F(Phi, A) = sigma{phi(x):x is an element of A} and the infinitesimal or germ sigma-field boolean AND(epsilon>0) F(Phi, A(epsilon)), where A(epsilon) is an epsilon-neighborhood of A. General analytic conditions are developed giving necessary and sufficient conditions for the equality of these two sigma-fields. These conditions are potent...
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作者：Bass, RF; Chen, ZQ
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：where W-t is d-dimensional Brownian motion with d greater than or equal to 2 and the ith component of At is a process of bounded variation that stands in the same relationship to a measure pi(i) as integral(0)(t) f(X-s) ds does to the measure f (x) dx. We prove weak existence and uniqueness for the above stochastic differential equation when the measures pi(i) are members of the Kato class Kd-1. As a typical example, we obtain a Brownian motion that has upward drift when in certain fractal-lik...
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作者：del Barrio, E; Giné, E; Matrán, C
作者单位：Universidad de Valladolid; University of Connecticut
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作者：Zambotti, L
作者单位：Scuola Normale Superiore di Pisa
摘要：We study a white-noise driven semilinear partial differential equation on the spatial interval [0, 1] with Dirichlet boundary condition and with a singular drift of the form cu(-3), c > 0. We prove existence and uniqueness of a non-negative continuous adapted solution u on [0, infinity) x [0, 1] for every nonnegative continuous initial datum x, satisfying x(0) = x(1) = 0. We prove that the law pi(delta) of the Bessel bridge on [0, 1] of dimension delta > 3 is the unique invariant probability m...
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作者：Roos, B
作者单位：University of Hamburg
摘要：We consider the approximation of the distribution of the sum of independent but not necessarily identically distributed random variables by a compound Poisson distribution and also by a finite signed measure of higher accuracy. Using Kerstan's method, some new bounds for the total variation distance are presented. Recently, several authors had difficulties applying Stein's method to the problem given. For instance, Barbour, Chen and Loh used this method in the case of random variables on the n...
