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作者：Crudu, A.; Debussche, A.; Muller, A.; Radulescu, O.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Universite de Montpellier
摘要：We study the asymptotic behavior of multiscale stochastic gene networks using weak limits of Markov jump processes. Depending on the time and concentration scales of the system, we distinguish four types of limits: continuous piecewise deterministic processes (PDP) with switching, PDP with jumps in the continuous variables, averaged PDP, and PDP with singular switching. We justify rigorously the convergence for the four types of limits. The convergence results can be used to simplify the stoch...
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作者：Pillai, Natesh S.; Stuart, Andrew M.; Thiery, Alexandre H.
作者单位：Harvard University; University of Warwick; University of Warwick
摘要：The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm which makes local moves by incorporating information about the gradient of the logarithm of the target density. In this paper we study the efficiency of MALA on a natural class of target measures supported on an infinite dimensional Hilbert space. These natural measures have density with respect to a Gaussian random field measure and arise in many applications such as Bayesian nonparametric statistics and the theory of c...
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作者：Bassetti, Federico; Ladelli, Lucia
作者单位：University of Pavia; Polytechnic University of Milan
摘要：This paper deals with a class of Boltzmann equations on the real line, extensions of the well-known Kac caricature. A distinguishing feature of the corresponding equations is that therein, the collision gain operators are defined by N-linear smoothing transformations. These kind of problems have been studied, from an essentially analytic viewpoint, in a recent paper by Bobylev, Cercignani and Gamba [Comm. Math. Phys. 291 (2009) 599-644]. Instead, the present work rests exclusively on probabili...
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作者：Cotar, Codina; Kuelske, Christof
作者单位：Ruhr University Bochum
摘要：We consider two versions of random gradient models. In model A the interface feels a bulk term of random fields while in model B the disorder enters through the potential acting on the gradients. It is well known that for gradient models without disorder there are no Gibbs measures in infinite-volume in dimension d = 2, while there are gradient Gibbs measures describing an infinite-volume distribution for the gradients of the field, as was shown by Funaki and Spohn. Van Enter and Kulske proved...
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作者：Mattingly, Jonathan C.; Pillai, Natesh S.; Stuart, Andrew M.
作者单位：Duke University; Duke University; Harvard University; University of Warwick
摘要：Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion ...
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作者：Denisov, D.; Foss, S.; Konstantopoulos, T.
作者单位：Cardiff University; Heriot Watt University; Uppsala University
摘要：We consider a stochastic directed graph on the integers whereby a directed edge between i and a larger integer j exists with probability p(j-i) depending solely on the distance between the two integers. Under broad conditions, we identify a regenerative structure that enables us to prove limit theorems for the maximal path length in a long chunk of the graph. The model is an extension of a special case of graphs studied in [Markov Process. Related Fields 9 (2003) 413-468]. We then consider a s...
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作者：Lember, Jueri; Matzinger, Heinrich; Torres, Felipe
作者单位：University of Tartu; University System of Georgia; Georgia Institute of Technology; University of Bielefeld
摘要：We consider a general class of superadditive scores measuring the similarity of two independent sequences of n i.i.d. letters from a finite alphabet. Our object of interest is the mean score by letter l(n). By subadditivity l(n) is nondecreasing and converges to a limit l. We give a simple method of bounding the difference l - l(n) and obtaining the rate of convergence. Our result generalizes the previous result of Alexander [Ann. Appl. Probab. 4 (1994) 1074-1082], where only the special case ...
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作者：Arguin, Louis-Pierre; Bovier, Anton; Kistler, Nicola
作者单位：Universite de Montreal; University of Bonn
摘要：As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time t, extremal particles descend with overwhelming probability from ancestors having split either within a distance of order 1 from time 0, or within a distance of order 1 from time t. The result suggests that the extremal process of branching Brownian motion is a randomly shifted cluster p...
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作者：Depperschmidt, Andrej; Greven, Andreas; Pfaffelhuber, Peter
作者单位：University of Freiburg; University of Erlangen Nuremberg
摘要：The Fleming-Viot measure-valued diffusion is a Markov process describing the evolution of (allelic) types under mutation, selection and random reproduction. We enrich this process by genealogical relations of individuals so that the random type distribution as well as the genealogical distances in the population evolve stochastically. The state space of this tree-valued enrichment of the Fleming-Viot dynamics with mutation and selection (TFVMS) consists of marked ultrametric measure spaces, eq...
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作者：Benaim, Michel; Faure, Mathieu
作者单位：University of Neuchatel
摘要：This paper considers a stochastic approximation algorithm, with decreasing step size and martingale difference noise. Under very mild assumptions, we prove the nonconvergence of this process toward a certain class of repulsive sets for the associated ordinary differential equation (ODE). We then use this result to derive the convergence of the process when the ODE is cooperative in the sense of Hirsch [SIAM J. Math. Anal. 16 (1985) 423-439]. In particular, this allows us to extend significantl...
