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作者：Foxall, Eric
作者单位：Arizona State University; Arizona State University-Tempe
摘要：We consider a stochastic model of infection spread incorporating monogamous partnership dynamics. In [Ann. AppL Probab. 26 (2016) 1297-1328], a basic reproduction number R-0 is defined with the property that if R-0 < 1 the infection dies out within O(log N) units of time, while if R-0 > 1 the infection survives for at least e(gamma N) units of time, for some gamma > 0. Here, we consider the critical case R-0 = 1 and show that the infection dies out within O (root N) units of time, and moreover...
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作者：Dick, Josef; Rudolf, Daniel; Zhu, Houying
作者单位：University of New South Wales Sydney; Friedrich Schiller University of Jena
摘要：Markov chains can be used to generate samples whose distribution approximates a given target distribution. The quality of the samples of such Markov chains can be measured by the discrepancy between the empirical distribution of the samples and the target distribution. We prove upper bounds on this discrepancy under the assumption that the Markov chain is uniformly ergodic and the driver sequence is deterministic rather than independent U(0, 1) random variables. In particular, we show the exis...
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作者：Ekstrom, Erik; Janson, Svante
作者单位：Uppsala University
摘要：Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that the solution of the inverse first-passage problem coincides with the solution of a related optimal stopping problem. Consequently, methods from optimal stopping theory may be applied in the study of the inverse first passage problem. We illustrate this with ...
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作者：Piiroinen, Petteri; Simon, Martin
作者单位：University of Helsinki; Johannes Gutenberg University of Mainz
摘要：In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman-Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman-Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated b...
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作者：Andrieu, Christophe; Vihola, Matti
作者单位：University of Bristol; University of Jyvaskyla
摘要：Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard MCMC algorithms, such as the target probability density in a Metropolis Hastings algorithm, with estimators. Perhaps surprisingly, such approximations lead to powerful algorithms which are exact in the sense that they are guaranteed to have correct limiting ...
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作者：Einarsson, Hafsteinn; Lengler, Johannes; Mousset, Frank; Panagiotou, Konstantinos; Steger, Angelika
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Munich
摘要：In an Achlioptas process, starting with a graph that has n vertices and no edge, in each round d >= 1 vertex pairs are chosen uniformly at random, and using some rule exactly one of them is selected and added to the evolving graph. We investigate the impact of the rule's choice on one of the most basic properties of a graph: connectivity. In our main result we focus on the prominent class of bounded size rules, which select the edge to add according to the component sizes of its vertices, trea...
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作者：Goldberg, David A.
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Recently, there has been significant interest in understanding the properties of Markov random fields (M.r.f.) defined on the independent sets of sparse graphs. When these M.r.f. are restricted to pairwise interactions (i.e., hardcore model), much progress has been made. However, considerably less is known in the presence of higher -order interactions, which arise, for example, in the analysis of independent sets with special properties and the study of resource-constrained communication netwo...
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作者：Bibinger, Markus; Jirak, Moritz; Reiss, Markus
作者单位：University of Mannheim; Humboldt University of Berlin
摘要：For a semi-martingale X-t, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation (X, X)(t) is constructed based on observations in the vicinity of X-t. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive n(-1/3) as optimal convergence rate in a high-frequency framework with n observations (in mean). We discuss a potential application for the estimation of the...
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作者：Cappelletti, Daniele; Wiuf, Carsten
作者单位：University of Copenhagen
摘要：We study networks of biochemical reactions modelled by continuous time Markov processes. Such networks typically contain many molecular species and reactions and are hard to study analytically as well as by simulation. Particularly, we are interested in reaction networks with intermediate species such as the substrate-enzyme complex in the Michaelis Menten mechanism. Such species are virtually in all real-world networks, they are typically short-lived, degraded at a fast rate and hard to obser...
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作者：Whiteley, Nick; Lee, Anthony
作者单位：University of Bristol; University of Warwick
摘要：We obtain a perfect sampling characterization of weak ergodicity for backward products of finite stochastic matrices, and equivalently, simultaneous tail triviality of the corresponding nonhomogeneous Markov chains. Applying these ideas to hidden Markov models, we show how to sample exactly from the finite-dimensional conditional distributions of the signal process given infinitely many observations, using an algorithm which requires only an almost surely finite number of observations to actua...
