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作者：Mason, David M.; Polonik, Wolfgang
作者单位：University of Delaware; University of California System; University of California Davis
摘要：We establish the asymptotic normality of the G-measure of the symmetric difference between the level set and a plug-in-type estimator of it formed by replacing the density in the definition of the level set by a kernel density estimator. Our proof will highlight the efficacy of Poissonization methods in the treatment of large sample theory problems of this kind.
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作者：Oliveira, Roberto Imbuzeiro
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We consider Kac's random walk on n-dimensional rotation matrices, where each step is a random rotation in the plane generated by two randomly picked coordinates. We show that this process converges to the Haar measure on SO(n) in the L-2 transportation cost (Wasserstein) metric in O(n(2) In n) steps. We also prove that our bound is at most a O(In n) factor away from optimal. Previous bounds, due to Diaconis/Saloff-Coste and Pak/Sidenko, had extra powers of n and held only for L-1 transportatio...
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作者：Meilijson, Isaac
作者单位：Tel Aviv University
摘要：Consider a random walk whose (light-tailed) increments have positive mean. Lower and upper bounds are provided for the expected maximal value of the random walk until it experiences a given drawdown d. These bounds, related to the Calmar ratio in finance, are of the form (exp{alpha d}-1)/alpha and (K exp{alpha d}-1)/alpha for some K > 1, in terms of the adjustment coefficient alpha (E[exp{-alpha X}] = 1) of the insurance risk literature. Its inverse 1/alpha has been recently derived by Aumann ...
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作者：Han, Guangyue; Marcus, Brian
作者单位：University of Hong Kong; University of British Columbia
摘要：We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop (2004) 117-122], we derive an asymptotic formula (when the noise parameter is small) for the entropy rate of a hidden Markov chain, observed when a Markov chain passes through a BSC. Using this res...
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作者：Blanchet, Jose H.
作者单位：Columbia University
摘要：Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we propose a methodology that can be used to design efficient importance sampling algorithms for counting and test their efficiency rigorously. We apply our techniques after transforming the problem into a rare-event simulation problem-thereby connecting complexity a...
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作者：Mayberry, John
作者单位：Cornell University
摘要：In this work, we examine spectral properties of Markov transition operators corresponding to Gaussian perturbations of discrete time dynamical systems on the circle. We develop a method for calculating asymptotic expressions for eigenvalues (in the zero noise limit) and show that changes to the number or period of stable orbits for the deterministic system correspond to changes in the number of limiting modulus 1 eigenvalues of the transition operator for the perturbed process. We call this ph...
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作者：Cerrai, Sandra
作者单位：University of Florence
摘要：We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite-dimensional systems.
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作者：du Toit, Jacques; Peskir, Goran
作者单位：University of Manchester
摘要：Assuming that the stock price Z = (Z(t))(0 <= t <= T) follows a geometric Brownian motion with drift mu is an element of R and volatility sigma > 0, and letting M-t = max(0 <= s <= t) Z(s) for t is an element of [0, T], we consider the optimal prediction problems V-1 = inf(0 <=tau <= T) E(M-T/Z(tau)) and V-2 = sup(0 <=tau <= T) E(Z(tau)/M-T), where the infimum and supremum are taken over all stopping times tau of Z. We show that the following strategy is optimal in the first problem: if mu <= ...
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作者：Greven, Andreas; Popovic, Lea; Winter, Anita
作者单位：University of Erlangen Nuremberg; Concordia University - Canada
摘要：We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate proportional to the number of catalyst individuals alive. The reactant forms a process in random medium. We describe asymptotically the genealogy of catalytic branching populations coded as the induced forest of R-trees using the many individuals-rapid branch...
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作者：Addario-Berry, Louigi; Broutin, Nicolas; Lugosi, Gabor
作者单位：Universite de Montreal; Pompeu Fabra University; ICREA; Pompeu Fabra University
摘要：We investigate the effective resistance R(n) and conductance C(n) between the root and leaves of a binary tree of height n. In this electrical network, the resistance of each edge e at distance d from the root is defined by r(e) = 2(d)X(e) where the X(e) are i.i.d. positive random variables bounded away from zero and infinity. It is shown that ER(n) = nEX(e) - (Var(X(e))/EX(e)) In n + O(1) and Var(R(n)) = O(1). Moreover, we establish sub-Gaussian tail bounds for R(n). We also discuss some poss...
