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作者：Graf, S; Luschgy, H
作者单位：University of Passau; Universitat Trier
摘要：For n, k is an element of N and r > 0 let e(n,r)(P-k)(r) = inf (1)/(k)(kSigmai=1) parallel toX(i) - f(X-i)parallel to(r), where the infimum is taken over all measurable maps f:R-d --> R-d with \f(R-d)\ less than or equal to n and X-1,..., X-k are i.i.d. R-d-valued random variables. We analyse the asymptotic a.s. behaviour of the nth empirical quantization error e(n,r)(P-k).
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作者：Sturm, KT
作者单位：University of Bonn
摘要：We develop a nonlinear martingale theory for time discrete processes (Y-n)(nis an element ofN0). These processes are defined on any filtered probability space (Omega, F, F-n, P)(nis an element ofN0) and have values in a metric space (N, d) of nonpositive curvature (in the sense of A. D. Alexandrov). The defining martingale property for such processes is E(Yn+1\F-n) = Y-n, P-a.s., where the conditional expectation on the left-hand side is defined as the minimizer of the functional Z --> Ed(2)(Z...
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作者：Flandoli, F; Russo, F
作者单位：University of Pisa; Universite Paris 13
摘要：Stochastic forward integrals for processes more general than semimartingales are shown to exist, generalized forms of Ito-Wentzell formula and covariation formula are proved, and one-dimensional stochastic equations driven by finite quadratic variation processes and semimartingales are solved. This generalized stochastic calculus is motivated by applications to uniqueness and dependence on parameters for stochastic equations with nonregular drift.
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作者：Khoshnevisan, D; Xiao, YM
作者单位：Utah System of Higher Education; University of Utah; Microsoft
摘要：We provide a probabilistic interpretation of a class of natural capacities on Euclidean space in terms of the level sets of a suitably chosen multiparameter additive Levy process X. We also present several probabilistic applications of the aforementioned potential-theoretic connections. They include areas such as intersections of Levy processes and level sets, as well as Hausdorff dimension computations.
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作者：Grandits, P; Rheinländer, T
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Let X be a locally bounded semimartingale. Using the theory of BMO-martingales we give a sufficient criterion for a martingale measure for X to minimize relative entropy among all martingale measures. This is applied to prove convergence of the q-optimal martingale measure to the minimal entropy martingale measure in entropy for q down arrow 1 under the assumption that X is continuous and that the density process of some equivalent martingale measure satisfies a reverse LLogL-inequality.
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作者：Barbour, AD; Cekanavicius, V
作者单位：University of Zurich; Vilnius University
摘要：Let W-n := Sigma(j-1)(n) (Zj) be a sum of independent integer-valued random variables. In this paper, we derive an asymptotic expansion for the probability P[W-n is an element of A] of an arbitrary subset A is an element of Z. Our approximation improves upon the classical expansions by including an explicit, uniform error estimate, involving only easily computable properties of the distributions of the Z(j): an appropriate number of moments and the total variation distance d(TV) (X (Zj), L(Z(j...
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作者：Bramson, M; Mountford, T
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：The product Bernoulli measures rho(alpha) with densities alpha, alpha is an element of [0, 1], are the extremal translation invariant stationary measures for an exclusion process with irreducible random walk kernel p((.)). In d = 1, stationary measures that are not translation invariant are known to exist for specific p((.)) satisfying Sigma(x) xp(x) > 0. These measures are concentrated on configurations that are completely occupied by particles far enough to the right and are completely empty...
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作者：Pittet, C; Saloff-Coste, L
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Cornell University
摘要：Wreath products are a type of semidirect product. They play an important role in group theory. This paper studies the basic behavior of simple random walks on such groups and shows that these walks have interesting, somewhat exotic behaviors. The crucial fact is that the probability of return to the starting point of certain walks on wreath products is closely related to some functionals of the local times of a walk taking place on a simpler factor group.
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作者：Bloznelis, M; Götze, F
作者单位：Vilnius University; University of Bielefeld
摘要：Let T be a symmetric statistic based on sample of size n drawn without replacement from a finite population of size N, where N > n. Assuming that the linear part of Hoeffding's decomposition of T is nondegenerate we construct a one term Edgeworth expansion for the distribution function of T and prove the validity of the expansion with the remainder O(1/n*) as n* --> infinity, where n* = min{n, N - n}.
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作者：Gravner, J; Tracy, CA; Widom, H
作者单位：University of California System; University of California Davis; University of California System; University of California Santa Cruz
摘要：We consider a model of interface growth in two dimensions, given by a height function on the sites of the one-dimensional integer lattice. According to the discrete time update rule, the height above the site x increases to the height above x - 1, if the latter height is larger; otherwise the height above x increases by I with probability p(x). We assume that p(x) are chosen independently at random with a common distribution F and that the initial state is such that the origin is far above the...
