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作者：Guan, Yongtao; Krone, Stephen M.
作者单位：University of Chicago; University of Idaho
摘要：We compare convergence rates of Metropolis-Hastings chains to multimodal target distributions when the proposal distributions can be of local and small world type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is slowly mixing (in the complexity of the problem) into a chain that is rapidly mixing. To do this, we obtain spectral gap estimates via a new state decomposition theorem and apply an isoperimetric ine...
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作者：Buraczewski, Dariusz
作者单位：University of Wroclaw
摘要：We consider an autoregressive model on R defined by the recurrence equation X-n = A(n)X(n-1) + B-n, where {(B-n, A(n))} are i.i.d. random variables valued in R x R+ and E[log A(1)] = 0 (critical case). It was proved by Babil-lot, Bougerol and Elie that there exists a unique invariant Radon measure of the process {X-n}. The aim of the paper is to investigate its behavior at infinity. We describe also stationary measures of two other stochastic recursions, including one arising in queuing theory.
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作者：Tracy, Craig A.; Widom, Harold
作者单位：University of California System; University of California Davis; University of California System; University of California Santa Cruz
摘要：We consider the process of n Brownian excursions conditioned to be nonintersecting. We show the distribution functions for the top curve and the bottom curve are equal to Fredholm determinants whose kernel we give explicitly. In the simplest case, these determinants are expressible in terms of Painleve V functions. We prove that as n -> infinity, the distributional limit of the bottom curve is the Bessel process with parameter 1/2. (This is the Bessel process associated with Dyson's Brownian m...
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作者：Duffie, Darrell; Sun, Yeneng
作者单位：Stanford University; National University of Singapore
摘要：This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has been popular in the economics and genetics literatures. We construct a joint agent-probability space, and randomized mutation, partial matching and match-induced type-changing functions that satisfy appropriate independence conditions. The proofs are achieved via nonstandard analysis. The proof for the dynamic setting relies on a new Fubini-type theorem ...
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作者：Caputo, Pietro; Faggionato, Alessandra
作者单位：Roma Tre University; Sapienza University Rome
摘要：We consider the random walk on a simple point process on R-d, d >= 2, whose jump rates decay exponentially in the alpha-power of jump length. The case alpha = 1 corresponds to the phonon-induced variable-range hopping in disordered solids in the regime of strong Anderson localization. Under mild assumptions on the point process, we show, for a epsilon (0, d), that the random walk confined to a cubic box of side L has a.s. Cheeger constant of order at least L-1 and mixing time of order L-2. For...
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作者：Dong, Rui; Gnedin, Alexander; Pitman, Jim
作者单位：University of California System; University of California Berkeley; Utrecht University
摘要：Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process and observed that similar methods could be applied to more complex models. Mohle described the recursion which determines the generalization of the Ewens sampling formula in the situation where the lines of descent are governed by a Lambda-coalescent, which allows mu...
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作者：Mayer-Wolf, Eddy; Zakai, Moshe
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：The model considered is that of signal plus white noise. Known connections between the noncausal filtering error and mutual information are combined with new ones involving the causal estimation error, in a general abstract setup. The results are shown to be invariant under a wide class of causality patterns; they are applied to the derivation of the causal estimation error of a Gaussian nonstationary filtering problem and to a multidimensional extension of the Yovits-Jackson formula.
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作者：Chigansky, Pavel; van Handel, Ramon
作者单位：Weizmann Institute of Science; California Institute of Technology
摘要：We investigate the robustness of nonlinear filtering for continuous time finite state Markov chains, observed in white noise, with respect to misspecification of the model parameters. It is shown that the distance between the optimal filter and that with incorrect model parameters converges to zero uniformly over the infinite time interval as the misspecified model converges to the true model, provided the signal obeys a mixing condition. The filtering error is controlled through the exponenti...
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作者：Roitershtein, Alexander
作者单位：University of British Columbia
摘要：For a class of stationary Markov-dependent sequences (A(n), B-n) is an element of R-2, we consider the random linear recursion S-n = A(n) + BnSn-1, n is an element of Z, and show that the distribution tail of its stationary solution has a power law decay.
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作者：Guyon, Julien
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of these individuals, we assume that the characteristic is stochastic and depends on its ancestors' only through the mother's characteristic. The dependency structure may be described by a transition probability P (x, dy dz) which gives the probability that the ...
