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作者：Clausel, Marianne; Coeurjolly, Jean-Francois; Lelong, Jerome
作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria
摘要：In this paper, we revisit the original ideas of Stein and propose an estimator of the intensity parameter of a homogeneous Poisson point process defined on R-d and observed on a bounded window. The procedure is based on a new integration by parts formula for Poisson point processes. We show that our Stein estimator outperforms the maximum likelihood estimator in terms of mean squared error. In many practical situations, we obtain a gain larger than 30%.
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作者：Delattre, Sylvain; Fournier, Nicolas; Hoffmann, Marc
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Universite PSL; Universite Paris-Dauphine
摘要：We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph G. The process is constructed as the solution to a system of Poisson driven stochastic differential equations, for which we prove pathwise existence and uniqueness under some reasonable conditions. We next investigate how to approximate a standard N-dimensional Hawkes process by a simple inhomogeneous Poisson process in the mean field framework where each pai...
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作者：Cerou, Frederic; Guyader, Arnaud
作者单位：Universite de Rennes; Universite de Rennes; Sorbonne Universite; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite de Rennes
摘要：Multilevel Splitting, also called Subset Simulation, is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel Splitting techniques. In contrast to their fixed level version, adaptive techniques estimate the sequence of levels on the fly and in an optimal way, with only a low additional computational cost. However, very few convergence res...
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作者：Podolskij, Mark; Yoshida, Nakahiro
作者单位：Aarhus University; Japan Science & Technology Agency (JST); Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for Studentized statistics of p...
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作者：Forde, Martin; Kumar, Rohini
作者单位：University of London; King's College London; Wayne State University
摘要：We establish a large-time large deviation principle (LDP) for a general mean-reverting stochastic volatility model with nonzero correlation and sublinear growth for the volatility coefficient, using the Donsker-Varadhan [Comm. Pure Appl. Math. 36 (1983) 183-212] LDP for the occupation measure of a Feller process under mild ergodicity conditions. We verify that these conditions are satisfied when the process driving the volatility is an Ornstein Uhlenbeck (013) process with a perturbed (subline...
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作者：Jaisson, Thibault; Rosenbaum, Mathieu
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Sorbonne Universite
摘要：We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has L-1 norm close to one and power law tail of the form x(-(1+alpha)), with alpha is an element of (0, 1). We in particular prove that when alpha is an element of (1/2, 1), after suitable rescaling, their law asymptotically behaves as a kind of integrated fractional Cox Ingersoll Ross process, with associated Hurst parameter H = alpha - 1/2. This result is in contrast to the case of a r...
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作者：Cetin, Umut; Danilova, Albina
作者单位：University of London; London School Economics & Political Science
摘要：This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse, the optimal strategies of the agents are solutions of a forward backward system of partial and stochastic differential equations. In particular, the price set by the market make...
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作者：Fang, Xiao; Siegmund, David
作者单位：National University of Singapore; Stanford University
摘要：As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables subject to possible change-points. Our formulation deals simultaneously with ordinary and with large deviations.
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作者：Verloop, I. M.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National Polytechnique de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We study the asymptotic optimal control of multi-class restless bandits. A restless bandit is a controllable stochastic process whose state evolution depends on whether or not the bandit is made active. Since finding the optimal control is typically intractable, we propose a class of priority policies that are proved to be asymptotically optimal under a global attractor property and a technical condition. We consider both a fixed population of bandits as well as a dynamic population where band...
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作者：Lejay, Antoine
作者单位：Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Inria; Universite de Lorraine
摘要：We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at 0 with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier. For this, we use a process called here the snapping out Brownian motion, whose properties are studied. As this construction is motivated by applications, for example, in brain imaging or in chemistry, a simulation scheme is also provided.
