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作者：Nutz, Marcel; Stebegg, Florian
作者单位：Columbia University
摘要：Two probability distributions p. and v in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are allowed as transports. Much like the Hoeffding-Frechet coupling of classical transport and its symmetric counterpart, the antitone coupling, these can be characterized by order-theore...
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作者：Rembart, Franz; Winkel, Matthias
作者单位：University of Oxford
摘要：We introduce a general recursive method to construct continuum random trees (CRTs) from independent copies of a random string of beads, that is, any random interval equipped with a random discrete probability measure, and from related structures. We prove the existence of these CRTs as a new application of the fixpoint method for recursive distribution equations formalised in high generality by Aldous and Bandyopadhyay. We apply this recursive method to show the convergence to CRTs of various ...
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作者：Paouris, Grigoris; Valettas, Petros
作者单位：Texas A&M University System; Texas A&M University College Station; University of Missouri System; University of Missouri Columbia
摘要：Let Z be an n-dimensional Gaussian vector and let f : R-n -> R be a convex function. We prove that P(f (Z) <= Ef (Z) - t root Var f(Z) <= = exp(-ct(2)), for all t > 1 where c > 0 is an absolute constant. As an application we derive variance-sensitive small ball probabilities for Gaussian processes.
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作者：Pal, Soumik; Wong, Ting-Kam Leonard
作者单位：University of Washington; University of Washington Seattle; University of Southern California
摘要：A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper, we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better gradient approximation than those of ordinary concave functions. The approximation error, called L-divergence, is different from the usual Bregman divergence. Using tools of information geometry a...
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作者：Cosso, Andrea; Federico, Salvatore; Gozzi, Fausto; Rosestolato, Mauro; Touzi, Nizar
作者单位：Polytechnic University of Milan; University of Siena; Luiss Guido Carli University; Luiss Guido Carli University; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Path-dependent partial differential equations (PPDEs) are natural objects to study when one deals with non-Markovian models. Recently, after the introduction of the so-called pathwise (or functional or Dupire) calculus [see Dupire (2009)], in the case of finite-dimensional underlying space various papers have been devoted to studying the well-posedness of such kind of equations, both from the point of view of regular solutions [see, e.g., Dupire (2009) and Cont (2016) Stochastic Integration by...
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作者：van Handel, Ramon
作者单位：Princeton University
摘要：The generic chaining method provides a sharp description of the suprema of many random processes in terms of the geometry of their index sets. The chaining functionals that arise in this theory are however notoriously difficult to control in any given situation. In the first paper in this series, we introduced a particularly simple method for producing the requisite multiscale geometry by means of real interpolation. This method is easy to use, but does not always yield sharp bounds on chainin...
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作者：Bolley, Francois; Gentil, Ivan; Guillin, Arnaud
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this work, we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this, we use optimal transport methods and the Borell-Brascamp-Lieb inequality. These refinements can be written as a deficit in the classical inequalities. They have the right scale with respect to the dimension. They lead to sharpened concentration properties as well as refined contraction bounds, convergence to equilibrium and short time behavior for the laws of solut...
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作者：Cammarota, Valentina; Marinucci, Domenico
作者单位：Sapienza University Rome; University of Rome Tor Vergata
摘要：We establish here a quantitative central limit theorem (in Wasserstein distance) for the Euler-Poincare characteristic of excursion sets of random spherical eigenfunctions in dimension 2. Our proof is based upon a decomposition of the Euler-Poincare characteristic into different Wiener-chaos components: we prove that its asymptotic behaviour is dominated by a single term, corresponding to the chaotic component of order two. As a consequence, we show how the asymptotic dependence on the thresho...
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作者：Gess, Benjamin; Hofmanova, Martina
作者单位：Max Planck Society; University of Bielefeld; Technical University of Berlin
摘要：We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full L-1 setting requiring no growth assumptions on the nonlinearities. In addition, we prove a comparison result and an L-1 -contraction property for the solution...
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作者：Tarrago, Pierre
作者单位：CIMAT - Centro de Investigacion en Matematicas
摘要：We investigate the asymptotic behavior of random paths on a graded graph which describes the subword order for words in two letters. This graph, denoted by Z, has been introduced by Viennot, who also discovered a remarkable bijection between paths on Z. and sequences of permutations. Later on, Gnedin and Olshanski used this bijection to describe the set of Gibbs measures on this graph. Both authors also conjectured that the Martin boundary of Z. should coincide with its minimal boundary. We gi...
