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作者：Burdzy, Krzysztof; Tadic, Tvrtko
作者单位：University of Washington; University of Washington Seattle; Microsoft; University of Zagreb
摘要：We consider two-dimensional and three-dimensional semi-infinite tubes made of Lambertian material, so that the distribution of the direction of a reflected light ray has the density proportional to the cosine of the angle with the normal vector. If the light source is far away from the opening of the tube then the exiting rays are (approximately) collimated in two dimensions but are not collimated in three dimensions. An observer looking into the three-dimensional tube will see infinitely brig...
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作者：Acciaio, Beatrice; Larsson, Martin
作者单位：University of London; London School Economics & Political Science; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a continuous-time financial market that consists of securities available for dynamic trading, and securities only available for static trading. We work in a robust framework where a set of non-dominated models is given. The concept of semi-static completeness is introduced: it corresponds to having exact replication by means of semi-static strategies. We show that semi-static completeness is equivalent to an extremality property, and give a characterization of the induced filtratio...
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作者：Dereich, Steffen; Mailler, Cecile; Morters, Peter
作者单位：University of Munster; University of Bath
摘要：We study a class of branching processes in which a population consists of immortal individuals equipped with a fitness value. Individuals produce offspring with a rate given by their fitness, and offspring may either belong to the same family, sharing the fitness of their parent, or be founders of new families, with a fitness sampled from a fitness distribution mu. Examples that can be embedded in this class are stochastic house-of-cards models, urn models with reinforcement and the preferenti...
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作者：Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C.
作者单位：University of Warwick; University of Geneva; University of Edinburgh
摘要：We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension d. The improved complexity is O(d(1/5)) compared to the complexity O(d(1/3)) of the standard approach. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate (with asymptotical va...
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作者：Heydenreich, Markus; Hulshof, Tim; Jorritsma, Joost
作者单位：University of Munich; Eindhoven University of Technology
摘要：Scale-free percolation is a percolation model on Z(d) which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience versus recurrence for dimension 1 and 2 and give sufficient conditions for transience in dimension 3 and higher. Finally, we show the existence of a hierarchical structure for parameters where vertices have degrees with infinite variance and obtain bounds on the cluster d...
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作者：El Karoui, Nicole; Loisel, Stephane; Salhi, Yahia
作者单位：Sorbonne Universite; Universite Claude Bernard Lyon 1
摘要：We consider the minimax quickest detection problem of an unobservable time of proportional change in the intensity of a doubly-stochastic Poisson process. We seek a stopping rule that minimizes the robust Lorden criterion, formulated in terms of the number of events until detection, both for the worst-case delay and the false alarm constraint. This problem, introduced by Page [Biometrika 41 (1954) 100-115], has received more attention in the continuous path framework (for Wiener processes) tha...
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作者：Lachieze-Rey, Raphael; Peccati, Giovanni
作者单位：Universite Paris Cite; University of Luxembourg
摘要：We obtain explicit Berry-Esseen bounds in the Kolmogorov distance for the normal approximation of nonlinear functionals of vectors of independent random variables. Our results are based on the use of Stein's method and of random difference operators, and generalise the bounds obtained by Chatter-jee (2008), concerning normal approximations in the Wasserstein distance. In order to obtain lower bounds for variances, we also revisit the classical Hoeffding decompositions, for which we provide a n...
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作者：Clement, Emmanuelle; Gloter, Arnaud
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; 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); Universite Paris Saclay
摘要：It is well known that the strong error approximation in the space of continuous paths equipped with the supremum norm between a diffusion process, with smooth coefficients, and its Euler approximation with step 1/n is O(n(-1/2)) and that the weak error estimation between the marginal laws at the terminal time T is O(n(-1)). An analysis of the weak trajectorial error has been developed by Alfonsi, Jourdain and Kohatsu-Higa [Ann. Appl. Probab. 24 (2014) 1049-1080], through the study of the p-Was...
