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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...
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作者：Lavancier, Frederic; Philippe, Anne
作者单位：Nantes Universite
摘要：Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our limit theorems and those of Ginovian (J. Contemp. Math. Anal. 34(2):1-15) to obtain the asymptotic behavior of the empirical covariances of Gaussian fields, which is a particular example of quadratic forms. We show that it is possible to obtain a Gaussian lim...
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作者：Ghosh, Subhankar; Goldstein, Larry
作者单位：University of Southern California
摘要：Let Y be a nonnegative random variable with mean mu and finite positive variance sigma(2), and let Y-s, defined on the same space as Y, have the Y size-biased distribution, characterized by E[Yf(Y)] = mu Ef(Y-s) for all functions f for which these expectations exist. Under a variety of conditions on Y and the coupling of Y and Ys, including combinations of boundedness and monotonicity, one sided concentration of measure inequalities such as p (Y - mu / sigma >= t) <= exp (-t(2) / 2(A + Bt) for...
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作者：Bossy, Mireille; Jabir, Jean-Francois; Talay, Denis
作者单位：Universite Cote d'Azur; Universidad de Chile
摘要：This paper is motivated by a new class of SDEs-PDEs systems, the so called Lagrangian stochastic models which are commonly used in the simulation of turbulent flows. We study a position-velocity system which is nonlinear in the sense of McKean. As the dynamics of the velocity depends on the conditional expectation with respect to its position, the interaction kernel is singular. We prove existence and uniqueness of the solution to the system by solving a nonlinear martingale problem and showin...
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作者：Mueller, Carl; Tribe, Roger
作者单位：University of Rochester; University of Warwick
摘要：In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is established to describe the large time evolution, distinguishing between certain death or possible life of the population.
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作者：Teixeira, Augusto
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In this paper, we establish some properties of percolation for the vacant set of random interlacements, for d a parts per thousand yen 5 and small intensity u. The model of random interlacements was first introduced by Sznitman in (Ann Math, arXiv:0704.2560, 2010). It is known that, for small u, almost surely there is a unique infinite connected component in the vacant set left by the random interlacements at level u, see Sidoravicius and Sznitman (Commun Pure Appl Math 62(6):831-858, 2009) an...
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作者：Mytnik, Leonid; Perkins, Edwin
作者单位：University of British Columbia; Technion Israel Institute of Technology
摘要：We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is Holder continuous of index gamma > 3/4. The method of proof is an infinite-dimensional version of the Yamada-Watanabe argument for ordinary stochastic differential equations.
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作者：Merlevede, Florence; Peligrad, Magda; Rio, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Ohio; University of Cincinnati
摘要：In this paper we present a Bernstein-type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviation results. Applications are given for classes of Markov chains, iterated Lipschitz models and functions of linear processes with absolutely regular innovations.
