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作者：Atar, Rami; Budhiraja, Amarjit
作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill
摘要：We study a class of stochastic control problems where a cost of the form E integral([0,infinity)) e(-beta s) [l(X-S)ds + h (Y-S degrees) d vertical bar Y vertical bar(s)] is to be minimized over control processes Y whose increments take values in a cone Y of RP, keeping the state process X = x + B + G Y in a cone X of R-k, k <= p. Here, x c X, B is a Brownian motion with drift b and covariance E, G is a fixed matrix, and Y degrees is the Radon-Nikodym derivative dY vertical bar d vertical bar ...
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作者：Janson, Svante
作者单位：Uppsala University
摘要：We study the characteristic function and moments of the integer-valued random variable [X + alpha], where X is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variables. This leads to oscillatory terms in asymptotics for these variables, something that has often been observed, for example in the analysis of several algorithms. We give som...
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作者：Goldstein, Larry; Xia, Aihua
作者单位：University of Southern California; University of Melbourne
摘要：We introduce a new family of distributions to approximate P(W epsilon A) for A subset of {...-2, -1, 0,1, 2...} and W a sum of independent integer-valued random variables xi(1), xi(2), ..., xi(n) with finite second moments, where, with large probability, W is not concentrated on a lattice of span greater than 1. The well-known Berry-Esseen theorem states that, for Z a normal random variable with mean E(W) and variance Var(W), P(Z epsilon A) provides a good approximation to P(W epsilon A) for A...
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作者：Ben Arous, Gerard; Voiculescu, Dan Virgil
作者单位：New York University; University of California System; University of California Berkeley
摘要：Free probability analogs of the basics of extreme-value theory are obtained, based on Ando's spectral order. This includes classification of freely max-stable laws and their domains of attraction, using free extremal convolutions on the distributions. These laws coincide with the limit laws in the classical peaks-over-threshold approach. A free extremal projection-valued process over a measure-space is constructed, which is related to the free Poisson point process.
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作者：Lyons, Russell; Peres, Yuval; Schramm, Oded
作者单位：Indiana University System; Indiana University Bloomington; University of California System; University of California Berkeley; Microsoft
摘要：Minimal spanning forests on infinite graphs are weak limits of minimal spanning trees from finite subgraphs. These limits can be taken with free or wired boundary conditions and are denoted FMSF (free minimal spanning forest) and WMSF (wired minimal spanning forest), respectively. The WMSF is also the union of the trees that arise from invasion percolation started at all vertices. We show that on any Cayley graph where critical percolation has no infinite clusters, all the component trees in t...
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作者：Gamburd, Alex
作者单位：University of California System; University of California Santa Cruz
摘要：Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a typical compact Riemann surface of large genus based on compactifying finite-area Riemann surfaces associated with random cubic graphs; by a theorem of Belyi, these are dense in the space of compact Riemann surfaces. The question as to how these surfaces are distributed in the Teichmuller spaces depends on the study o...
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作者：Szarek, Tomasz
摘要：We consider Feller processes on a complete separable metric space X satisfying the ergodic condition of the form limsup n ->infinity (1/n Sigma P-n(i=1)i(x, 0)) > 0 for some x epsilon X, where O is an arbitrary open neighborhood of some point z epsilon X and P is a transition function. It is shown that e-chains which satisfy the above condition admit an invariant probability measure. Some results on the stability of such processes are also presented.
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作者：Karlsson, Anders; Ledrappier, Francois
作者单位：Royal Institute of Technology; University of Notre Dame
摘要：We prove a general noncommutative law of large numbers. This applies in particular to random walks on any locally finite homogeneous graph, as well as to Brownian motion on Riemannian manifolds which admit a compact quotient. It also generalizes Oseledec's multiplicative ergodic theorem. In addition, we show that epsilon-shadows of any ballistic random walk with finite moment on any group eventually intersect. Some related results concerning Coxeter groups and mapping class groups are recorded...
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作者：Graham, B. T.; Grimmett, G. R.
作者单位：University of Cambridge
摘要：The influence theorem for product measures on the discrete space to, {0, 1}(N) may be extended to probability measures with the property of monotonicity (which is equivalent to strong positive association). Corresponding results are valid for probability measures on the cube [0, 1](N) that are absolutely continuous with respect to Lebesgue measure. These results lead to a sharp-threshold theorem for measures of random-cluster type, and this may be applied to box crossings in the two-dimensiona...
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作者：Mytnik, Leonid; Perkins, Edwin; Sturm, Anja
作者单位：Technion Israel Institute of Technology; University of British Columbia; University of Delaware
摘要：We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on R-d for d >= 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Holder continuity of the solutions near zero is established.
