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作者：Dombry, Clement; Hashorva, Enkelejd; Soulier, Philippe
作者单位：Universite Marie et Louis Pasteur; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Lausanne
摘要：The goal of this paper is an exhaustive investigation of the link between the tail measure of a regularly varying time series and its spectral tail process, independently introduced in [Owada and Samorodnitsky (2012)] and [Stochastic Process. Appl. 119 (2009) 1055-1080]. Our main result is to prove in an abstract framework that there is a one-to-one correspondence between these two objects, and given one of them to show that it is always possible to build a time series of which it will be the ...
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作者：Doney, R. A.; Griffin, Philip S.
作者单位：University of Manchester; Syracuse University
摘要：The reflected process of a random walk or Levy process arises in many areas of applied probability, and a question of particular interest is how the tail of the distribution of the heights of the excursions away from zero behaves asymptotically. The Levy analogue of this is the tail behaviour of the characteristic measure of the height of an excursion. Apparently, the only case where this is known is when Cramer's condition hold. Here, we establish the asymptotic behaviour for a large class of...
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作者：Mendelson, Shahar; Rauhut, Holger; Ward, Rachel
作者单位：Technion Israel Institute of Technology; Australian National University; RWTH Aachen University; University of Texas System; University of Texas Austin
摘要：We study the recovery of sparse vectors from subsampled random convolutions via l(1)-minimization. We consider the setup in which both the subsampling locations as well as the generating vector are chosen at random. For a sub-Gaussian generator with independent entries, we improve previously known estimates: if the sparsity s is small enough, that is, s less than or similar to root n/log(n), we show that m greater than or similar to s log(en/s) measurements are sufficient to recover s-sparse v...
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作者：Chenavier, Nicolas; Robert, Christian Y.
作者单位：Universite du Littoral-Cote-d'Opale; Universite Claude Bernard Lyon 1
摘要：We consider the Voronoi tessellation based on a homogeneous Poisson point process in an Euclidean space. For a geometric characteristic of the cells (e.g., the inradius, the circumradius, the volume), we investigate the point process of the nuclei of the cells with large values. Conditions are obtained for the convergence in distribution of this point process of exceedances to a homogeneous compound Poisson point process. We provide a characterization of the asymptotic cluster size distributio...
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作者：El Euch, Omar; Rosenbaum, Mathieu
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under rough volatility can be intricate since the dynamics involve fractional Brownian motion. We show in this paper that surprisingly enough, explicit hedging strategies can be obtained in the case of rough Heston models. The replicating portfolios contain the underl...
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作者：Eldan, Ronen; Gross, Renan
作者单位：Weizmann Institute of Science
摘要：We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of an associated functional, thereby satisfying a certain matrix equation. In the dense regime, every solution to this equation is close to a block matrix, concluding that the exponential random graph behaves roughly like a mixture of stochastic block models. We...
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作者：Federico, Salvatore; Gozzi, Fausto
作者单位：University of Siena; Luiss Guido Carli University
摘要：Verification theorems are key results to successfully employ the dynamic programming approach to optimal control problems. In this paper, we introduce a new method to prove verification theorems for infinite dimensional stochastic optimal control problems. The method applies in the case of additively controlled Ornstein-Uhlenbeck processes, when the associated Hamilton-Jacobi-Bellman (HJB) equation admits a mild solution (in the sense of [J. Differential Equations 262 (2017) 3343-3389]). The m...
