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作者：Douc, Randal; Moulines, Eric; Olsson, Jimmy
作者单位：Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; IMT Atlantique; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT Atlantique; Royal Institute of Technology
摘要：This paper discusses particle filtering in general hidden Markov models (HMMs) and presents novel theoretical results on the long-term stability of bootstrap-type particle filters. More specifically, we establish that the asymptotic variance of the Monte Carlo estimates produced by the bootstrap filter is uniformly bounded in time. On the contrary to most previous results of this type, which in general presuppose that the state space of the hidden state process is compact (an assumption that i...
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作者：Briand, Philippe; Labart, Celine
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Universite Savoie Mont Blanc; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We present an algorithm to solve BSDEs based on Wiener chaos expansion and Picard's iterations. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. We use the Malliavin derivative to compute Z. Concerning the error, we derive explicit bounds with respect to the number of chaos and the discretization time step. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.
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作者：Fedrizzi, Ennio
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schrodinger and Korteweg-de Vries equations under random perturbations of the initial conditions: for a wide class of rapidly oscillating random perturbations this problem reduces to the study of a canonical system of stochastic differential equations which depends only on the integrated covariance of the perturbation. We finally stud...
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作者：Roberts, Gareth O.; Rosenthal, Jeffrey
作者单位：University of Warwick; University of Toronto
摘要：We derive new results comparing the asymptotic variance of diffusions by writing them as appropriate limits of discrete-time birth death chains which themselves satisfy Peskun orderings. We then apply our results to simulated tempering algorithms to establish which choice of inverse temperatures minimises the asymptotic variance of all functionals and thus leads to the most efficient MCMC algorithm.
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作者：Borodin, Alexei; Corwin, Ivan
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS
摘要：We study the parabolic Anderson model in (1 + 1) dimensions with nearest neighbor jumps and space time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders.
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作者：Gruebel, Rudolf
作者单位：Leibniz University Hannover
摘要：We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces converge with probability 1. This is then used to obtain almost sure convergence for various tree functionals, together with representations of the respective limit random variables as functions of the limit tree.
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作者：Hegarty, Peter; Martinsson, Anders
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：We present rigorous mathematical analyses of a number of well-known mathematical models for genetic mutations. In these models, the genome is represented by a vertex of the n-dimensional binary hypercube, for some n, a mutation involves the flipping of a single bit, and each vertex is assigned a real number, called its fitness, according to some rules. Our main concern is with the issue of existence of (selectively) accessible paths; that is, monotonic paths in the hypercube along which fitnes...
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作者：Penda, S. Valere Bitseki; Djellout, Hacene; Guillin, Arnaud
作者单位：Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Universitaire de France
摘要：First, under a geometric ergodicity assumption, we provide some limit theorems and some probability inequalities for the bifurcating Markov chains (BMC). The BMC model was introduced by Guyon to detect cellular aging from cell lineage, and our aim is thus to complete his asymptotic results. The deviation inequalities are then applied to derive first result on the moderate deviation principle (MDP) for a functional of the BMC with a restricted range of speed, but with a function which can be un...
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作者：Shah, D.; Walton, N. S.; Zhong, Y.
作者单位：Massachusetts Institute of Technology (MIT); University of Amsterdam; Columbia University
摘要：We consider a switched (queuing) network in which there are constraints on which queues may be served simultaneously; such networks have been used to effectively model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time, based on the current state or past history of the system. In the main result of this paper, we provide a new class of online scheduling policies that achieve optimal queue-size scaling for a...
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作者：Kang, Weining; Ramanan, Kavita
作者单位：University System of Maryland; University of Maryland Baltimore; Brown University
摘要：Given a domain G, a reflection vector field d(center dot) on partial derivative G, the boundary of G; and drift and dispersion coefficients b(center dot) and sigma(center dot), let L be the usual second-order elliptic operator associated with b(center dot) and sigma(center dot). Under mild assumptions on-the coefficients and reflection vector field, it is shown that when the associated submartingale problem is well posed, a probability measure pi on (G) over bar with pi (partial derivative G) ...
