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作者：Li, Xiang-Dong
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Fudan University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Based on a new martingale representation formula, we prove some quantitative upper bound estimates of the L (p) -norm of some singular integral operators on complete Riemannian manifolds. This leads us to establish the Weak L (p) -Hodge decomposition theorem and to prove the L (p) -boundedness of the Beurling-Ahlfors transforms on complete non-compact Riemannian manifolds with non-negative Weitzenbock curvature operator.
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作者：Daskalakis, Constantinos; Mossel, Elchanan; Roch, Sebastien
作者单位：University of California System; University of California Los Angeles; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley; Weizmann Institute of Science
摘要：A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct the leaf-labelled tree. It is well known that in order to reconstruct a tree on n leaves, sample sequences of length Omega (log n) are needed. It was conjectured by Steel that for the CFN/Ising evolutionary model, if the mutation probability on all edges of...
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作者：Buchmann, Boris; Maller, Ross
作者单位：Monash University; Australian National University
摘要：We give a small time functional version of Chung's other law of the iterated logarithm for L,vy processes with non-vanishing Brownian component. This is an analogue of the other law of the iterated logarithm at large times for L,vy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.
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作者：Baraud, Yannick
作者单位：Universite Cote d'Azur
摘要：We observe a random measure N and aim at estimating its intensity s. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random vector with nonnegative components and the intensity of a Poisson process. Our estimation strategy is based on estimator selection. Given a family of estimators of s based on the observation of N, we propose a selection rule, based on N as well, in view of selec...
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作者：Frei, Christoph; Malamud, Semyon; Schweizer, Martin
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Institut Polytechnique de Paris; Ecole Polytechnique; Swiss Finance Institute (SFI); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider backward stochastic differential equations (BSDEs) with a particular quadratic generator and study the behaviour of their solutions when the probability measure is changed, the filtration is shrunk, or the underlying probability space is transformed. Our main results are upper bounds for the solutions of the original BSDEs in terms of solutions to other BSDEs which are easier to solve. We illustrate our results by applying them to exponential utility indifference valuation in a mul...
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作者：Kallenberg, Olav
作者单位：Auburn University System; Auburn University
摘要：Let G be a measurable group with Haar measure., acting properly on a space S and measurably on a space T. Then any sigma-finite, jointly invariant measure M on S x T admits a disintegration nu circle times mu into an invariant measure nu on S and an invariant kernel mu from S to T. Here we construct nu and mu by a general skew factorization, which extends an approach by Rother and Zahle for homogeneous spaces S over G. This leads to easy extensions of some classical propositions for invariant ...
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作者：Sabot, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Z(d), RWDE are parameterized by a 2d-uplet of positive reals. We prove that for all values of the parameters, RWDE are transient in dimension d >= 3. We also prove that the Green function has some finite moments and we characterize the finite moments. Our result is more general and appli...
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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：For a stationary Poisson-Voronoi tessellation in Euclidean d-space and for k is an element of {1, ... , d}, we consider the typical k-dimensional face with respect to a natural centre function. We express the distribution of this typical k-face in terms of a certain Poisson process of closed halfspaces in a k-dimensional space. Then we show that, under the condition of large inradius, the relative boundary of the typical k-face lies, with high probability, in a narrow spherical annulus.
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作者：Benjamini, Itai; Nachmias, Asaf; Peres, Yuval
作者单位：Weizmann Institute of Science; Microsoft
摘要：We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. We also prove a finite analogue of this statement, valid for expander graphs, without any girth assumption.
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作者：Bassetti, Federico; Ladelli, Lucia; Matthes, Daniel
作者单位：Polytechnic University of Milan; University of Pavia; Technische Universitat Wien
摘要：We introduce a class of kinetic-type equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with rather general properties. By establishing a connection to the central limit problem, we are able to prove long-time convergence of the equation's solutions toward a limit distribution. For example, we prove that if the initial condition belongs to the domain of normal attraction of a certain s...
