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作者：Doebler, Christian; Kasprzak, Mikolaj J.; Peccati, Giovanni
作者单位：Heinrich Heine University Dusseldorf; University of Luxembourg
摘要：We consider sequences of U-processes based on symmetric kernels of a fixed order, that possibly depend on the sample size. Our main contribution is the derivation of a set of analytic sufficient conditions, under which the aforementioned U-processes weakly converge to a linear combination of time-changed independent Brownian motions. In view of the underlying symmetric structure, the involved time-changes and weights remarkably depend only on the order of the U-statistic, and have consequently...
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作者：Dombry, Clement; Tillier, Charles; Wintenberger, Olivier
作者单位：Universite Marie et Louis Pasteur; Universite Paris Saclay; Universite Paris Cite; Sorbonne Universite
摘要：We consider regular variation for marked point processes with independent heavy-tailed marks and prove a single large point heuristic: the limit measure is concentrated on the cone of point measures with one single point. We then investigate successive hidden regular variation removing the cone of point measures with at most k points, k >= 1, and prove a multiple large point phenomenon: the limit measure is concentrated on the cone of point measures with k + 1 points. We show how these results...
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作者：Bo, Lijun; Liao, Huafu; Yu, Xiang
作者单位：Xidian University; National University of Singapore; Hong Kong Polytechnic University
摘要：This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated under partial observations of asset prices and sequential default events. By establishing a martingale representation theorem based on incomplete and phasing out filtration, we c...
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作者：De Angelis, Tiziano; Merkulov, Nikita; Palczewski, Jan
作者单位：University of Turin; University of Leeds
摘要：We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general cadlag measurable processes. As a by-product of our method of proof we also obtain existence of optimal strategies for both players. The main novelties are that we do not assume a Markovian nature of the game nor a particular structure of the information available to the players. This allows us to go beyon...
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作者：Bhattacharjee, Chinmoy; Schulte, Matthias
作者单位：University of Luxembourg; Hamburg University of Technology
摘要：We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observation window and show that its limiting distribution is Frechet. We achieve this by proving convergence of the underlying point process of the degrees to a certain Poisson process. Estimating the index of the power-law tail for the typical degree distribution is an important question in statistics. We prove consistency o...
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作者：Louart, Cosme; Couillet, Romain
作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
摘要：This article studies the robust covariance matrix estimation of a data collection X = (x1, ... , xn) with xi = /tau izi + m, where zi is an element of Rp is a con-centrated vector (e.g., an elliptical random vector), m is an element of Rp a deterministic signal and tau i is an element of R a scalar perturbation of possibly large amplitude, under the assumption where both n and p are large. This estimator is defined as the fixed point of a function which we show is contracting for a so-called s...
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作者：Penda, S. Valere Bitseki; Delmas, Jean-Francois
作者单位：Universite Bourgogne Europe; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive functionals of BMC, and prove the existence of three regimes. This corresponds to a competition between the reproducing rate (each individual has two children) and the ergodicity rate for the evolution of the trait. This is in contrast with the work of Guyon (Ann. ...
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作者：Broutin, Nicolas; Duquesne, Thomas; Wang, Minmin
作者单位：Universite Paris Cite; Sorbonne Universite; University of Sussex
摘要：Motivated by limits of critical inhomogeneous random graphs, we construct a family of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the multiplicative coalescent (the Erdos-Renyi random graph, more generally the so-called rank-one inhomogeneous random graphs of various types, and the configuration model). At the discrete level, the construction relies on a new point of view on (discrete) inhomogeneous rand...
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作者：Bouchard, Bruno; Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Chinese University of Hong Kong
摘要：We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (SIAM J. Control Optim. 57 (2019) 4125-49), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under strong regularity conditions. Using only probabilistic arguments, we prove, in a path-dependent setting and under weak regularity conditions, that any solution to this dual problem actually allows one to construct explici...
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作者：Curato, Imma Valentina; Stelzer, Robert; Stroeh, Bennet
作者单位：Ulm University
摘要：We obtain central limit theorems for stationary random fields employing a novel measure of dependence called theta-lex weak dependence. We show that this dependence notion is more general than strong mixing, that is, it applies to a broader class of models. Moreover, we discuss hereditary properties for theta-lex and eta-weak dependence and illustrate the possible applications of the weak dependence notions to the study of the asymptotic properties of stationary random fields. Our general resu...
