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作者：Kargin, Vladislav
作者单位：Stanford University
摘要：Suppose that X(1), ... , X(n), ... are i.i.d. rotationally invariant N-by-N matrices. Let Pi(n) = X(n) ... X(1). It is known that n(-1) log vertical bar Pi(n)vertical bar converges to a non-random limit. We prove that under certain additional assumptions on matrices X(i) the speed of convergence to this limit does not decrease when the size of matrices, N, grows.
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作者：Lemaire, Vincent; Pages, Gilles
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
摘要：We propose an unconstrained stochastic approximation method for finding the optimal change of measure (in an a priori parametric family) to reduce the variance of a Monte Carlo simulation. We consider different parametric families based on the Girsanov theorem and the Esscher transform (exponential-tilting). In [Monte Carlo Methods Appl. 10 (2004) 1-24], it described a projected Robbins-Monro procedure to select the parameter minimizing the variance in a multidimensional Gaussian framework. In...
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作者：Schopp, Eva-Maria
作者单位：University of Freiburg
摘要：In this paper we prove a functional limit theorem for the weighted profile of a b-ary tree. For the proof we use classical martingales connected to branching Markov processes and a generalized version of the profile-polynomial martingale. By embedding, choosing weights and a branch factor in a right way, we finally rediscover the profiles of some well-known discrete time trees.
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作者：Cox, J. Theodore
作者单位：Syracuse University
摘要：We consider the stepping stone model on the torus of side L in Z(2) in the limit L -> infinity, and study the time it takes two lineages tracing backward in time to coalesce. Our work fills a gap between the finite range migration case of [Ann. Appl. Probab 15 (2005) 671-699] and the long range case of [Genetics 172 (2006) 701-708], where the migration range is a positive fraction of L. We obtain limit theorems for the intermediate case, and verify a conjecture in [Probability Models for DNA S...
