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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：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：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：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：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.
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作者：Pfaffelhuber, P.; Wakolbinger, A.; Weisshaupt, H.
作者单位：University of Freiburg; Goethe University Frankfurt; University of Freiburg
摘要：A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the sum of the branch lengths, briefly denoted as tree length, and prove that the (suitably compensated) sequence of tree length processes converges, as the population size tends to infinity, to a limit process with cA dlA g paths, infinite infinitesimal varian...
