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作者：Adler, Robert; Samorodnitsky, Gennady
作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; Cornell University
摘要：We describe the mean rate at which a general absolutely continuous stationary S alpha S process crosses a high level. Only nondegeneracy assumptions are imposed in the case 1 < alpha < 2. The same results hold for 0 < alpha <= 1 under certain conditions, ensuring existence of the required conditional moments and the applicability of the classical integral formula for the expected number of level crossings.
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作者：Penrose, Mathew D.
作者单位：Durham University
摘要：For n points placed uniformly at random on the unit square, suppose M-n (respectively, M-n(1)) denotes the longest edge-length of the nearest neighbor graph (respectively, the minimal spanning tree) on these points. It is known that the distribution of n pi M-n(2) - log n converges weakly to the double exponential; we give a new proof of this. We show that P[M-n(1) = M-n] -> 1, so that the same weak convergence holds for M-n(1).
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作者：Bramson, Maury; Neuhauser, Claudia
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider a two-dimensional catalytic surface reaction between X and Y-n with Y-n + nX -> nXY, where Y-n is a polymer consisting of n identical atoms, each denoted by Y, and X is a monomer. The reactants X and Y-n are present above the surface in a gaseous phase, and bond to the surface at certain rates. The resulting atoms X and Y on the surface react if they are sufficiently close to each other; the product XY then leaves the surface, A classical example is the oxidation of carbon monoxide...
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作者：Carmona, Rene A.; Xu, Lin
作者单位：Princeton University
摘要：We consider the diffusive scaling limit for the transport of a passive scalar in a two-dimensional time-dependent incompressible Gaussian velocity field and in the presence of molecular diffusivity. We prove that homogenization holds in this limiting regime and we derive some simple properties of the effective diffusivity tensor.
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作者：Komorowski, Tomasz; Papanicolaou, George
作者单位：Michigan State University; Stanford University
摘要：We prove that the solution of a system of random ordinary differential equations dX(t)/dt = V(t, X(t) with diffusive scaling, X-epsilon(t) = epsilon X(t/epsilon(2)), converges weakly to a Brownian motion when epsilon down arrow 0. We assume that V(t,X), t is an element of R, X is an element of R-d is a d-dimensional, random, incompressible, stationary Gaussian field which has mean zero and decorrelates in finite time.
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作者：Schmidli, H.
作者单位：Aarhus University
摘要：In applied probability one is often interested in the asymptotic behavior of a certain quantity. If a regenerative phenomenon can be imbedded, then one has the problem that the event of interest may have occurred but cannot be observed at the renewal points. In this paper an extension to the renewal theorem is proved which shows that the quantity of interest converges. As an illustration an open problem in risk theory is solved.
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作者：Goldstein, Larry; Reinert, Gesine
作者单位：University of Southern California; University of Southern California
摘要：Let W be a random variable with mean zero and variance sigma(2). The distribution of a variate W*, satisfying EWf(W). = sigma 2Ef' (W*). for smooth functions f, exists uniquely and defines the zero bias transformation on the distribution of W. The zero bias transformation shares many interesting properties with the well-known size bias transformation for nonnegative variables, but is applied to variables taking on both positive and negative values. The transformation can also be defined on mor...
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作者：Calvin, James M.
作者单位：New Jersey Institute of Technology
摘要：We describe a class of adaptive algorithms for approximating the global minimum of a continuous function on the unit interval. The limiting distribution of the error is derived under the assumption of Wiener measure on the objective functions. For any delta > 0, we construct an algorithm which has error converging to zero at rate n(-(1-delta)) in the number of function evaluations n. This convergence rate contrasts with the n(-1/2) rate of previously studied nonadaptive methods.
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作者：Hall, Peter; Raimondo, Marc
作者单位：Australian National University; Commonwealth Scientific & Industrial Research Organisation (CSIRO)
摘要：Throw a straight line at random into a plane, within which is inscribed a square grid. Color black each grid vertex that lies above the line, and white each vertex below it. Now remove the line, and attempt to reconstruct it from the pattern of vertex colors in an m x m section of the grid. We show that for all epsilon > 0, the line can be approximated to within order m(-1) (log m)(log log m)(1+epsilon), with probability 1, and that there is no deterministic subsequence along which the best ac...
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作者：Stefanov, V. T.; Pakes, A. G.
作者单位：University of Western Australia
摘要：A new and unified approach is presented for constructing joint generating functions for quantities of interest associated with pattern formation in binary sequences. The method is based on results on exponential families of Markov chains. The tools we use are not only new for this area; they seem to be the right approach for deriving general explicit distributional results.
