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作者：Leao, Dorival; Ohashi, Alberto
作者单位：Universidade de Sao Paulo; Universidade Federal da Paraiba
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作者：Bai, Lihua; Ma, Jin; Xing, Xiaojing
作者单位：Nankai University; University of Southern California
摘要：In this paper, we study a class of optimal dividend and investment problems assuming that the underlying reserve process follows the Sparre Andersen model, that is, the claim frequency is a renewal process, rather than a standard compound Poisson process. The main feature of such problems is that the underlying reserve dynamics, even in its simplest form, is no longer Markovian. By using the backward Markovization technique, we recast the problem in a Markovian framework with expanded dimensio...
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作者：Tadic, Vladislav B.; Doucet, Arnaud
作者单位：University of Bristol; University of Oxford
摘要：The asymptotic behavior of the stochastic gradient algorithm using biased gradient estimates is analyzed. Relying on arguments based on dynamic system theory (chain-recurrence) and differential geometry (Yomdin theorem and Lojasiewicz inequalities), upper bounds on the asymptotic bias of this algorithm are derived. The results hold under mild conditions and cover a broad class of algorithms used in machine learning, signal processing and statistics.
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作者：Bayer, Christian; Horst, Ulrich; Qiu, Jinniao
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; University of Michigan System; University of Michigan
摘要：We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges in distribution to a fully coupled SDE-SPDE system when the order arrival rates tend to infinity and the impact of an individual order arrival...
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作者：Antunovic, Tonci; Procaccia, Eviatar B.
作者单位：University of California System; University of California Los Angeles; Texas A&M University System; Texas A&M University College Station
摘要：We consider two stationary versions of the Eden model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. Under weak assumptions on the weight distribution and by relying on ergodic theorems, we prove that almost surely all trees are finite. Using the mass transport principle, we generalize the result to Eden model in graphs of the form G x z(+), where G is a Cayley graph. This generalizes certain known results on the two-type Richardson model, in partic...
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作者：Franco, Tertuliano; Neumann, Adriana
作者单位：Universidade Federal da Bahia; Universidade Federal do Rio Grande do Sul
摘要：We consider the one-dimensional symmetric simple exclusion process with a slow bond. In this model, whilst all the transition rates are equal to one, a particular bond, the slow bond, has associated transition rate of value N-1, where N is the scaling parameter. This model has been considered in previous works on the subject of hydrodynamic limit and fluctuations. In this paper, assuming uniqueness for weak solutions of hydrodynamic equation associated to the perturbed process, we obtain dynam...
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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：Matzinger, Heinrich; Pachon, Angelica; Popov, Serguei
作者单位：University System of Georgia; Georgia Institute of Technology; University of Turin; Universidade Estadual de Campinas
摘要：We consider a d-dimensional scenery seen along a simple symmetric branching random walk, where at each time each particle gives the color record it observes. We show that up to equivalence the scenery can be reconstructed a.s. from the color record of all particles. To do so, we assume that the scenery has at least 2d + 1 colors which are i.i.d. with uniform probability. This is an improvement in comparison to Popov and Pachon [Stochastics 83 (2011) 107-116], where at each time the particles n...
