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作者：Barbu, Viorel; Roeckner, Michael; Russo, Francesco
作者单位：Alexandru Ioan Cuza University; University of Bielefeld; Purdue University System; Purdue University; Institut Polytechnique de Paris; ENSTA Paris
摘要：We consider a possibly degenerate porous media type equation over all of R-d with d = 1, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analyti...
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作者：Bally, Vlad; Clement, Emmanuelle
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We establish an integration by parts formula in an abstract framework in order to study the regularity of the law for processes arising as the solution of stochastic differential equations with jumps, including equations with discontinuous coefficients for which the Malliavin calculus developed by Bichteler et al. (Stochastics Monographs, vol 2. Gordon & Breach, New York, 1987) and Bismut (Z Wahrsch Verw Gebiete 63(2):147-235, 1983) fails.
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作者：Hairer, M.; Mattingly, J. C.; Scheutzow, M.
作者单位：University of Warwick; New York University; Duke University; Technical University of Berlin
摘要：There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal assumptions on one hand and the existence of a spectral gap under conditions reminiscent of Harris' theorem. The first uses the existence of couplings which draw the solutions together as time goes to infinity. Such asymptotic couplings were central to (Mattingly and Sinai...
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作者：Collet, Pierre; Martinez, Servet; Meleard, Sylvie; San Martin, Jaime
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universidad de Chile; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric space. Each individual can die or generate a new individual. The birth and death rates may depend on the environment through the action of the whole population. The offspring can have the same trait or can mutate to a randomly distributed trait. We assume that th...
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作者：Betz, Volker; Ueltschi, Daniel
作者单位：University of Warwick
摘要：We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in the space and there is an additional weight that involves the length of permutation jumps. We prove the occurrence of infinite macroscopic cycles above a certain critical density.
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作者：Alberts, Tom; Sheffield, Scott
作者单位：University of Toronto; Massachusetts Institute of Technology (MIT)
摘要：We construct a natural measure mu supported on the intersection of a chordal SLE(kappa) curve gamma with R, in the range 4 < kappa < 8. The measure is a function of the SLE path in question. Assuming that boundary measures transform in a d-dimensional way (where d is the Hausdorff dimension of gamma boolean AND R), we show that the measure we construct is (up to multiplicative constant) the unique measure-valued function of the SLE path that satisfies the Domain Markov property.
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作者：Heydenreich, Markus; van der Hofstad, Remco
作者单位：Vrije Universiteit Amsterdam; Eindhoven University of Technology
摘要：For critical bond-percolation on high-dimensional torus, this paper proves sharp lower bounds on the size of the largest cluster, removing a logarithmic correction in the lower bound in Heydenreich and van der Hofstad (Comm Math Phys 270(2):335-358, 2007). This improvement finally settles a conjecture by Aizenman (Nuclear Phys B 485(3):551-582, 1997) about the role of boundary conditions in critical high-dimensional percolation, and it is a key step in deriving further properties of critical p...
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作者：van Handel, Ramon
作者单位：Princeton University
摘要：We show that large-scale typicality of Markov sample paths implies that the likelihood ratio statistic satisfies a law of iterated logarithm uniformly to the same scale. As a consequence, the penalized likelihood Markov order estimator is strongly consistent for penalties growing as slowly as log log n when an upper bound is imposed on the order which may grow as rapidly as log n. Our method of proof, using techniques from empirical process theory, does not rely on the explicit expression for ...
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作者：Addario-Berry, L.; Broutin, N.
作者单位：McGill University
摘要：We consider a branching random walk for which the maximum position of a particle in the n'th generation, R-n, has zero speed on the linear scale: R-n/n -> 0 as n -> infinity. We further remove (kill) any particle whose displacement is negative, together with its entire descendence. The size Z of the set of un-killed particles is almost surely finite (Gantert and Muller in Markov Process. Relat. Fields 12:805-814, 2006; Hu and Shi in Ann. Probab. 37(2):742-789, 2009). In this paper, we confirm ...
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作者：Boucheron, Stephane; Massart, Pascal
作者单位：Universite Paris Saclay; Sorbonne Universite; Universite Paris Cite
摘要：A theorem by Wilks asserts that in smooth parametric density estimation the difference between the maximum likelihood and the likelihood of the sampling distribution converges toward a Chi-square distribution where the number of degrees of freedom coincides with the model dimension. This observation is at the core of some goodness-of-fit testing procedures and of some classical model selection methods. This paper describes a non-asymptotic version of the Wilks phenomenon in bounded contrast op...
