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作者：Harnett, Daniel; Nualart, David
作者单位：University of Kansas
摘要：The purpose of this paper is to establish the convergence in law of the sequence of midpoint Riemann sums for a stochastic process of the form f'(W), where W is a Gaussian process whose covariance function satisfies some technical conditions. As a consequence we derive a change-of-variable formula in law with a second order correction term which is an Ito integral of f ''(W) with respect to a Gaussian martingale independent of W. The proof of the convergence in law is based on the techniques o...
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作者：Barrieu, Pauline; El Karoui, Nicole
作者单位：University of London; London School Economics & Political Science; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：In this paper, we study the stability and convergence of some general quadratic semimartingales. Motivated by financial applications, we study simultaneously the semimartingale and its opposite. Their characterization and integrability properties are obtained through some useful exponential sub-martingale inequalities. Then, a general stability result, including the strong convergence of the martingale parts in various spaces ranging from H-1 to BMO, is derived under some mild integrability co...
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作者：Emilia Caballero, M.; Perez Garmendia, Jose Luis; Uribe Bravo, Geronimo
作者单位：Universidad Nacional Autonoma de Mexico; Instituto Tecnologico Autonomo de Mexico; Universidad Nacional Autonoma de Mexico
摘要：Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a representation of continuous-state branching processes with immigration by solving a random ordinary differential equation driven by a pair of independent Levy processes. Stability of the solutions is studied and gives, in particular, limit theorems (of a type prev...
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作者：Mester, Peter
作者单位：Indiana University System; Indiana University Bloomington
摘要：We show by example that there is a Cayley graph, having two invariant random subgraphs X and Y, such that there exists a monotone coupling between them in the sense that X subset of Y, although no such coupling can be invariant. Here, invariant means that the distribution is invariant under group multiplications.
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作者：Pavlov, Ronnie
作者单位：University of British Columbia
摘要：For any two-dimensional nearest neighbor shift of finite type X and any integer n >= 1, one can define the horizontal strip shift H-n (X) to be the set of configurations on Z x {1, ... , n} which do not contain any forbidden pairs of adjacent letters for X. It is always the case that the sequence h(top)(H-n(X))/n of normalized topological entropies of the strip shifts converges to h(toP)(X), the topological entropy of X. In this paper, we combine ergodic theoretic techniques with methods from ...
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作者：Romik, Dan
作者单位：University of California System; University of California Davis
摘要：The arctic circle theorem of Jockusch, Propp, and Shor asserts that uniformly random domino tilings of an Aztec diamond of high order are frozen with asymptotically high probability outside the arctic circle inscribed within the diamond. A similar arctic circle phenomenon has been observed in the limiting behavior of random square Young tableaux. In this paper, we show that random domino tilings of the Aztec diamond are asymptotically related to random square Young tableaux in a more refined s...
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作者：Graf, Siegfried; Luschgy, Harald; Pages, Gilles
作者单位：University of Passau; Universitat Trier; Universite Paris Cite; Sorbonne Universite
摘要：For a large class of absolutely continuous probabilities P it is shown that, for r > 0, for n-optimal L-r (P)-codebooks alpha(n), and any Voronoi partition V-n,V-a with respect to alpha(n) the local probabilities P(V-n,V-a) satisfy P(V-a,V-n) approximate to n(-1) while the local L-r-quantization errors satisfy integral V-n,V-a parallel to x - a parallel to(r) d P (x) approximate to n(-(1+r/d)) as long as the partition sets V-n,V-a intersect a fixed compact set K in the interior of the support ...
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作者：Kern, Peter; Meerschaert, Mark M.; Scheffler, Hans-Peter
作者单位：Heinrich Heine University Dusseldorf; Michigan State University; Universitat Siegen
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作者：Banica, Teodor; Curran, Stephen; Speicher, Roland
作者单位：CY Cergy Paris Universite; University of California System; University of California Los Angeles; Queens University - Canada; Saarland University
摘要：We study sequences of noncommutative random variables which are invariant under quantum transformations coming from an orthogonal quantum group satisfying the easiness condition axiomatized in our previous paper. For 10 easy quantum groups, we obtain de Finetti type theorems characterizing the joint distribution of any infinite quantum invariant sequence. In particular, we give a new and unified proof of the classical results of de Finetti and Freedman for the easy groups S-n, O-n, which is ba...
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作者：Grimmett, Geoffrey R.; Holroyd, Alexander E.
作者单位：University of Cambridge; University of British Columbia; Microsoft
摘要：Does there exist a Lipschitz injection of Z(d) into the open set of a site percolation process on Z(D), if the percolation parameter p is sufficiently close to 1? We prove a negative answer when d = D and also when d >= 2 if the Lipschitz constant M is required to be I. Earlier work of Dirr, Dondl, Grimmett, Holroyd and Scheutzow yields a positive answer for d < D and M = 2. As a result, the above question is answered for all d, D and M. Our proof in the case d = D uses Tucker's lemma from top...
