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作者：Gaunt, Robert E.; Pickett, Alastair M.; Reinert, Gesine
作者单位：University of Oxford
摘要：This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve both the shape parameter and the order of the derivative. Subsequently, Stein's method for chi-square approximation is applied to bound the distributional distance between Pearson's statistic and its limiting chi-square distribution, measured using smooth te...
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作者：Birkner, Matthias; Sun, Rongfeng
作者单位：Johannes Gutenberg University of Mainz; National University of Singapore
摘要：We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat equation and predicts that starting from the empty configuration the total number of particles grows as c root t logt. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.
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作者：Goncalves, Patricia; Landim, Claudio; Milanes, Aniura
作者单位：Universidade de Lisboa; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal de Minas Gerais
摘要：We consider one-dimensional, boundary driven, weakly asymmetric exclusion processes in contact with reservoirs at fixed density. For a general set of initial measures and by using a microscopic Cole-Hopf transformation, we derive the nonequilibrium fluctuations which are given by a generalized Ornstein-Uhlenbeck process.
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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：Bayraktar, Erhan; Ya, Song
作者单位：University of Michigan System; University of Michigan; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We analyze a robust version of the Dynkin game over a set P of mutually singular probabilities. We first prove that conservative player's lower and upper value coincide (let us denote the value by V). Such a result connects' the robust Dynkin game with second-order doubly reflected backward stochastic differential equations. Also, we show that the value process V is a submartingale under an appropriately defined nonlinear expectation E up to the first time tau* when V meets the lower payoff pr...
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作者：Jenkins, Paul A.; Spano, Dario
作者单位：University of Warwick; University of Warwick
摘要：The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article, we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition...
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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...
