The Annals of Applied Probability

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• Transition times and stochastic resonance for multidimensional diffusions with time periodic drift: A large deviations approach AI翻译
  作者：Herrmann, Samuel; Imkeller, Peter; Peithmann, Dierk
  作者单位：Universite de Lorraine; Humboldt University of Berlin
  摘要：We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period T and a small Gaussian random perturbation of intensity 8, and, therefore, are mathematically described as weakly time inhomogeneous diffusion processes. A system is in stochastic resonance, provided the small noisy perturbation is tuned in such a way that its random trajectories follow the exterior perio...
• Learning nonsingular phylogenies and hidden Markov models AI翻译
  作者：Mossel, Elchanan; Roch, Sebastien
  作者单位：University of California System; University of California Berkeley
  摘要：In this paper we study the problem of learning phylogenies and hidden Markov models. We call a Markov model nonsingular if all transition matrices have determinants bounded away from 0 (and 1). We highlight the role OF of the nonsingularity condition for the learning problem. Learning hidden Markov models without the nonsingularity condition is at least as hard as learning parity with noise a well-known learning problem conjectured to be computationally hard. On the other hand, we give a polyn...
• The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance AI翻译
  作者：Blum, Michael G. B.; Francois, Olivier; Janson, Svante
  作者单位：Uppsala University; Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble
  摘要：For two decades, the Colless index has been the most frequently used statistic for assessing the balance of phylogenctic trees. In this article, this statistic is studied under the Yule and uniform model of phylogenetic trees. The main tool of analysis is a coupling argument with another well-known index called the Sackin statistic. Asymptotics for the mean, variance and covariance of these two statistics are obtained, as well as their limiting joint distribution for large phylogenies. Under t...
• Theoretical framework for the pricing of contingent claims in the presence of model uncertainty AI翻译
  作者：Denis, Laurent; Martini, Claude
  作者单位：Universite Paris Saclay
  摘要：The aim of this work is to evaluate the cheapest superreplication price of a general (possibly path-dependent) European contingent claim in a context where the model is uncertain. This setting is a generalization of the uncertain volatility model (UVM) introduced in by Avellaneda. Levy and Paras. The uncertainty is specified by a family of martingale probability measures which may not be dominated. we obtain a partial characterization result and a full characterization which extends Avellaneda...
• Mean field convergence of a model of multiple TCP connections through a buffer implementing red AI翻译
  作者：McDonald, DR; Reynier, J
  作者单位：University of Ottawa; Universite PSL; Ecole Normale Superieure (ENS)
  摘要：RED (Random Early Detection) has been suggested when multiple TCP sessions are multiplexed through a bottleneck buffer, The idea is to detect congestion before the buffer overflows by dropping or marking packets with a probability that increases with the queue length. The objectives are reduced packet loss, higher throughput, reduced delay and reduced delay variation achieved through an equitable distribution of packet loss and reduced synchronization. Baccelli, McDonald and Reynier [Performan...
• Error estimates for binomial approximations of game options (vol 16, pg 984, 2006) AI翻译
  作者：Kifer, Yuri
  作者单位：Hebrew University of Jerusalem
• A new coexistence result for competing contact processes AI翻译
  作者：Chan, Benjamin; Durrett, Richard
  作者单位：Cornell University
  摘要：Neuhauser [Probab. Theory Related Fields 91 (1992) 467-506] considered the two-type contact process and showed that on Z(2) coexistence is not possible if the death rates are equal and the particles use the same dispersal neighborhood. Here, we show that it is possible for a species with a long-, but finite, range dispersal kernel to coexist with a superior competitor with nearest-neighbor dispersal in a model that includes deaths of blocks due to forest fires.
• On the variational distance of two trees AI翻译
  作者：Steel, M. A.; Szekely, L. A.
  作者单位：University of Canterbury; University of South Carolina System; University of South Carolina Columbia
  摘要：A widely studied model for generating sequences is to evolve them on a tree according to a symmetric Markov process. We prove that model trees tend to be maximally far apart in terms of variational distance.
• Limitations of Markov chain Monte Carlo algorithms for Bayesian inference of phylogeny AI翻译
  作者：Mossel, Elchanan; Vigoda, Eric
  作者单位：University of California System; University of California Berkeley; University System of Georgia; Georgia Institute of Technology
  摘要：Markov chain Monte Carlo algorithms play a key role in the Bayesian approach to phylogenetic inference. In this paper, we present the first theoretical work analyzing the rate of convergence of several Markov chains widely used in phylogenetic inference. We analyze simple, realistic examples where these Markov chains fail to converge quickly. In particular, the data studied are generated from a pair of trees, under a standard evolutionary model. We prove that many of the popular Markov chains ...
• Tail asymptotics for the maximum of perturbed random walk AI翻译
  作者：Araman, Victor F.; Glynn, Peter W.
  作者单位：New York University; Stanford University
  摘要：Consider a random walk S=(S-n:n >= 0) that is perturbed by a stationary sequence (xi(n): n >= 0) to produce the process (S-n+xi(n):n >= 0). This paper is concerned with computing the distribution of the all-time maximum M-infinity= max{S-k+xi(k):k >= 0) of perturbed random walk with a negative drift. Such a maximum arises in several different applications settings, including production systems, communications networks and insurance risk. Our main results describe asymptotics for P(M-infinity >...