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作者：Fathi, Max; Maas, Jan
作者单位：Sorbonne Universite; Institute of Science & Technology - Austria
摘要：We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and death chains, product chains, Bernoulli-Laplace models, and random transposition models). However, a general method to obtain discrete Ricci bounds had been lacking. Our method covers all of the examples above. In addition, we obtain new Ricci curvature bou...
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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：Hoffman, Christopher; Johnson, Tobias; Junge, Matthew
作者单位：University of Washington; University of Washington Seattle; University of Southern California
摘要：Consider the following interacting particle system on the d-ary tree, known as the frog model: Initially, one particle is awake at the root and i.i.d. Poisson many particles are sleeping at every other vertex. Particles that are awake perform simple random walks, awakening any sleeping particles they encounter. We prove that there is a phase transition between transience and recurrence as the initial density of particles increases, and we give the order of the transition up to a logarithmic fa...
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作者：Najim, Jamal; Yao, Jianfeng
作者单位：Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); ESIEE Paris; Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
摘要：Consider a N x n matrix Sigma(n) = 1 root n R-n(1/2) X-n, where R-n is a nonnegative definite Hermitian matrix and X-n is a random matrix with i.i.d. real or complex standardized entries. The fluctuations of the linear statistics of the eigenvalues Trace f (Sigma(n) Sigma(n)*) = Sigma(N)(i=1) f (lambda(i)), (lambda(i)) eigenvalues of Sigma(n) Sigma(n)*, are shown to be Gaussian, in the regime where both dimensions of matrix Sigma(n) go to infinity at the same pace and in the case where f is of...
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作者：Dereich, Steffen; Li, Sangmeng
作者单位：University of Munster
摘要：In this article, we consider multilevel Monte Carlo for the numerical computation of expectations for stochastic differential equations driven by Levy processes. The underlying numerical schemes are based on jump adapted Euler schemes. We prove stable convergence of an idealised scheme. Further, we deduce limit theorems for certain classes of functionals depending on the whole trajectory of the process. In particular, we allow dependence on marginals, integral averages and the supremum of the ...
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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：McKeague, Ian W.; Levin, Bruce
作者单位：Columbia University
摘要：From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the interaction of finitely many classical worlds. The wave function is then recovered (as a secondary object) from observations of particles in these worlds, without knowing the world from which any particular observation originates. Hall, Deckert and Wiseman [Phys. R...
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作者：Henry-Labordere, Pierre; Obloj, Jan; Spoida, Peter; Touzi, Nizar
作者单位：University of Oxford; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We obtain bounds on the distribution of the maximum of a martingale with fixed marginals at finitely many intermediate times. The bounds are sharp and attained by a solution to n-marginal Skorokhod embedding problem in Obloj and Spoida [An iterated Azema-Yor type embedding for finitely many marginals (2013) Preprint]. It follows that their embedding maximizes the maximum among all other embeddings. Our motivating problem is superhedging lookback options under volatility uncertainty for an inve...
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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 ...
