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作者：Yan, Jun
作者单位：Stanford University
摘要：By extending (Adv. Math. 299 (2016) 396-450), we present a framework to calculate large deviations for nonlinear functions of independent random variables supported on compact sets in Banach spaces. Previous research on nonlinear large deviations has only focused on random variables supported on {-1, +1}(n), and accordingly we build theory for random variables with general distributions, increasing flexibility in the applications. As examples, we compute the large deviation rate functions for ...
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作者：Buijsrogge, Anne; Dupuis, Paul; Snarski, Michael
作者单位：University of Twente; Brown University
摘要：In this paper we study the performance of splitting algorithms, and in particular the RESTART method, for the numerical approximation of the probability that a process leaves a neighborhood of a metastable point during some long time interval [0, T]. We show that, in contrast to alternatives such as importance sampling, the decay rate of the second moment does not degrade as T -> infinity. In the course of the analysis we develop some related large deviation estimates that apply when the time ...
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作者：Harris, Simon C.; Horton, Emma; Kyprianou, Andreas E.
作者单位：University of Auckland; Universite de Lorraine; University of Bath
摘要：The neutron transport equation (NTE) describes the flux of neutrons across a planar cross-section in an inhomogeneous fissile medium when the process of nuclear fission is active. Classical work on the NTE emerges from the applied mathematics literature in the 1950s through the work of R. Dautray and collaborators (Methodes Probabilistes Pour les equations de la Physique (1989) Eyrolles; Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 6: Evolution Problems. II (199...
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作者：Peres, Yuval; Racz, Miklos Z.; Sly, Allan; Stuhl, Izabella
作者单位：Princeton University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：It is well known that sequential decision making may lead to information cascades. That is, when agents make decisions based on their private information, as well as observing the actions of those before them, then it might be rational to ignore their private signal and imitate the action of previous individuals. If the individuals are choosing between a right and a wrong state, and the initial actions are wrong, then the whole cascade will be wrong. This issue is due to the fact that cascades...
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作者：Ngo, Hoang-Long; Taguchi, Dai
作者单位：Hanoi National University of Education; University of Osaka
摘要：We introduce a semi-implicit Euler-Maruyama approximation which preserves the noncolliding property for some class of noncolliding particle systems such as Dyson-Brownian motions, Dyson-Ornstein-Uhlenbeck processes and Brownian particle systems with nearest neighbor repulsion, and study its rates of convergence in both L-p-norm and pathwise sense.
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作者：Dyszewski, Piotr; Mikosch, Thomas
作者单位：University of Wroclaw; Technical University of Munich; University of Copenhagen
摘要：It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation property of product-type functions of regularly varying random vectors, generalizing and extending the univariate theory in various directions. The main result is then applied to characterize the regular variation property of products of i.i.d. regularly varyin...
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作者：Han, Ruijian; Ye, Rougang; Tan, Chunxi; Chen, Kani
作者单位：Hong Kong University of Science & Technology
摘要：The Bradley-Terry model is a fundamental model in the analysis of network data involving paired comparison. Assuming every pair of subjects in the network have an equal number of comparisons, Simons and Yao (Ann. Statist. 27 (1999) 1041-1060) established an asymptotic theory for statistical estimation in the Bradley-Terry model. In practice, when the size of the network becomes large, the paired comparisons are generally sparse. The sparsity can be characterized by the probability p(n) that a ...
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作者：Dupuis, Paul; Katsoulakis, Markos A.; Pantazis, Yannis; Rey-Bellet, Luc
作者单位：Brown University; University of Massachusetts System; University of Massachusetts Amherst; Foundation for Research & Technology - Hellas (FORTH)
摘要：Rare events play a key role in many applications and numerous algorithms have been proposed for estimating the probability of a rare event. However, relatively little is known on how to quantify the sensitivity of the rare event's probability with respect to model parameters. In this paper, instead of the direct statistical estimation of rare event sensitivities, we develop novel and general uncertainty quantification and sensitivity bounds which are not tied to specific rare event simulation ...
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作者：Barrera, Gerardo; Jara, Milton
作者单位：University of Alberta; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation converges exponentially fast to an equilibrium distribution. We show that the convergence occurs abruptly: in a time window of small size compared to the natural time scale of the process, the distance to equilibrium drops from its maximal possible value to ne...
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作者：Bou-Rabee, Nawaf; Eberle, Andreas; Zimmer, Raphael
作者单位：Rutgers University System; Rutgers University Camden; University of Bonn
摘要：Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L-1 Wasserstein) distance. The lower bound for the contraction rate is explicit. Global convexity of the potential is not required, and thus multimodal target distributions are included. Explicit quantitative bounds for the number of steps required to approximate the stationary distribution up to a given error epsilon are a direct ...
