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作者：Farre, Merce; Jolis, Maria; Utzet, Frederic
作者单位：Autonomous University of Barcelona
摘要：In the framework of vector measures and the combinatorial approach to stochastic multiple integral introduced by Rota and Wallstrom [Ann. Probab. 25 (1997) 1257-1283], we present an Ito multiple integral and a Stratonovich multiple integral with respect to a Levy process with finite moments up to a convenient order. In such a framework, the Stratonovich multiple integral is an integral with respect to a product random measure whereas the Ito multiple integral corresponds to integrate with resp...
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作者：Comets, Francis; Popov, Serguei; Schuetz, Gunter M.; Vachkovskaia, Marina
作者单位：Universite Paris Cite; Universidade Estadual de Campinas; Helmholtz Association; Research Center Julich
摘要：We consider a stochastic billiard in a random tube which stretches to infinity in the direction of the first coordinate. This random tube is stationary and ergodic, and also it is supposed to be in some sense well behaved. The stochastic billiard can be described as follows: when strictly inside the tube, the particle moves straight with constant speed. Upon hitting the boundary, it is reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the...
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作者：Berestycki, Julien; Berestycki, Nathanael; Limic, Vlada
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：Consider a Lambda-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number N-t of blocks at any positive time t > 0). We exhibit a deterministic function v: (0, infinity) -> (0, infinity) such that N-t/v(t) -> 1, almost surely, and in L-p for any p >= 1, as t -> 0. Our approach relies on a novel martingale technique.
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作者：Chen, Xia; Li, Wenbo V.; Marcus, Michael B.; Rosen, Jay
作者单位：University of Tennessee System; University of Tennessee Knoxville; City University of New York (CUNY) System; City College of New York (CUNY); University of Delaware; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：Let {L-t(x); (x, t) is an element of R-1 x R-+(1)} denote the local time of Brownian motion, and alpha(t) := integral(infinity)(-infinity)(L-t(x))(2)dx. Let eta = N(0, 1) be independent of alpha(t). For each fixed t, integral(infinity)(-infinity)(L-t(x+h) - L-t(x))(2) dx - 4ht/h(3/2) L -> (64/3)(1/2) root alpha(t)eta as h -> 0. Equivalently, integral(infinity)(-infinity)(L-t(x+1) - L-t(x))(2) dx - 4t/t(3/4) L -> (64/3)(1/2) root alpha(1)eta as t -> infinity.
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作者：Barany, Imre; Reitzner, Matthias
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London; University Osnabruck
摘要：We prove the central limit theorem for the volume and the f-vector of the Poisson random polytope Pi(eta) in a fixed convex polytope P subset of R(d) Here, Pi(eta) is the convex hull of the intersection of a Poisson process X of intensity eta with P
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作者：Komorowski, Tomasz; Peszat, Szymon; Szarek, Tomasz
作者单位：Maria Curie-Sklodowska University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Fahrenheit Universities; University of Gdansk
摘要：We formulate a criterion for the existence and uniqueness of an invariant measure for a Markov process taking values in a Polish phase space In addition. weak-* ergodicity, that is, the weak convergence of the ergodic averages of of the laws of the process starting from any initial distribution, is established The principal assumptions are the existence of a lower bound for the ergodic averages of the transition probability function and its local uniform continuity The latter is called the e-p...
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作者：Hug, Daniel; Schneider, Rolf
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Freiburg
摘要：A generalized version of a well-known problem of D. G. Kendall states that the zero cell of a stationary Poisson hyperplane tessellation in R(d), under the condition that it has lame volume, approximates with high probability a certain definite shape, which is determined by the directional distribution of the underlying hyperplane process. This result is extended here to typical k-faces of the tessellation, for k is an element of {2, ... , d - 1}. This requires the additional condition that th...
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作者：Buergisser, Peter; Cucker, Felipe; Lotz, Martin
作者单位：University of Paderborn; City University of Hong Kong; University of Oxford
摘要：This paper has two agendas. Firstly, we exhibit new results for coverage processes. Let p(n, m, alpha) be the probability that n spherical caps of angular radius alpha in S-m do not cover the whole sphere S-m. We give an exact formula for p (n, m, alpha) in the case alpha is an element of [pi/2, pi] and an upper bound for p(n, m, alpha) in the case alpha is an element of [0, pi/2] which tends to p(n, m, pi/2) when alpha -> pi/2. In the case alpha is an element of [0, pi/2] this yields upper bo...
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作者：Wang, Jiun-Chau
作者单位：Queens University - Canada
摘要：In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands We prove not only the uniform convergence of the densities to the semicircular density but also their L-P-convergence to the same limit for p > 1/2 Moreover, an entropic central limit theorem is obtained as a consequence of the above results
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作者：Bjorklund, Michael
作者单位：Royal Institute of Technology
摘要：We generalize the asymptotic shape theorem in first passage percolation on Z(d) to cover the case of general semimetrics. We prove a structure theorem for equivariant semimetrics on topological groups and an extended version of the maximal inequality for Z(d)-cocycles of Boivin and Derriennic in the vector-valued case. This inequality will imply a very general form of Kingman's subadditive ergodic theorem. For certain classes of generalized first passage percolation, we prove further structure...
