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作者：Talagrand, M
作者单位：University System of Ohio; Ohio State University
摘要：The concentration of measure phenomenon in product spaces is a far-reaching abstract generalization of the classical exponential inequalities for sums of independent random variables. We attempt to explain in the simplest possible terms the basic concepts underlying this phenomenon, the basic method to prove concentration inequalities and the meaning of several of the most useful inequalities.
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作者：ArenalGutierrez, E; Matran, C
摘要：We develop a new technique to prove the conditional CLT for the weighted bootstrap mean. Through 0-1 laws, we show that this conditional CLT can be derived from an unconditional one which easily arises (conditioning with respect to the weights) from the standard Lindeberg CLT.
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作者：Deheuvels, P; Einmahl, JHJ
作者单位：Eindhoven University of Technology
摘要：We prove functional laws of the iterated logarithm for empirical processes based upon censored data in the neighborhood of a fixed point. We apply these results to obtain strong laws for estimators of local functionals of the lifetime distribution. In particular, we describe the pointwise strong limiting behavior of the kernel density estimator based upon the Kaplan-Meier product-limit estimator.
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作者：Kallianpur, G; Xiong, J
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We consider the random fields X(epsilon)(t, q), t greater than or equal to 0, q is an element of O, governed by stochastic partial differential equations driven by a Gaussian white noise in space-time, where O is a bounded domain in R(d) with regular boundary. To study the continuity of the random fields X(epsilon) in space and time variables, we prove an analogue of Garsia's theorem. We then derive the large deviation results based on the methods used by the second author in another paper. Th...
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作者：deHaan, L; Resnick, S
作者单位：Cornell University
摘要：Rates of convergence of the distribution of the extreme order statistic to its limit distribution are given in the uniform metric and the total variation metric. A second-order regular variation condition is imposed by supposing a von Mises type condition which allows a unified treatment. Rates are constructed from the parameters of the second-order regular variation condition. Some connections with Poisson processes are discussed.
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作者：Komorowski, T
作者单位：New York University
摘要：In this paper we prove several theorems concerning the motion of a particle in a random environment. The trajectory of a particle is the solution of the differential equation dx(t)/dt = V(x(t)), where V(x) = v + epsilon(1-alpha) F(x), 0 less than or equal to alpha < 1, v is a constant vector, F is a mean-zero fluctuation field and epsilon(1-alpha) is a parameter measuring the size of the fluctuations. We show that both in case of a motion of a single particle and of a particle system considere...
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作者：Licea, C; Newman, CM
作者单位：New York University
摘要：We consider standard first-passage percolation on Z(2). Geodesics are nearest-neighbor paths in Z(2), each of whose segments is time-minimizing. We prove part of the conjecture that doubly infinite geodesics do not exist. Our main tool is a result of independent interest about the coalescing of semi-infinite geodesics.
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作者：Schweizer, M
摘要：Let X be a semimartingale and let Theta be the space of all predictable X-integrable processes theta such that integral theta dX is in the space L(2) of semimartingales. We consider the problem of approximating a given random variable H is an element of L(2)(P) by the sum of a constant c and a stochastic integral integral(0)(T) theta(s), dX(s), with respect to the L(2)(P)-norm. This problem comes from financial mathematics, where the optimal constant V-0 can be interpreted as an approximation ...
