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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：Budhiraja, Amarjit; Ghosh, Arka P.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Iowa State University
摘要：Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control problems, that have been proposed as approximate models for the study of these critically loaded controlled stochastic networks, can be regarded as formal scaling limits of such stochastic systems. However, to date, a rigorous limit theory that justifies the use o...
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作者：Belius, David
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：This note investigates cover levels of finite sets in the random interlacements model introduced in [Ann. of Math. (2) 171 (2010) 2039-2087], that is, the least level such that the set is completely contained in the random interlacement at that level. It proves that as the cardinality of a set goes to infinity, the resealed and recentered cover level tends in distribution to the Gumbel distribution with cumulative distribution function exp(-exp(-z)).
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作者：Borrello, Davide
作者单位：University of Milano-Bicocca; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of Z(d). In each of the four models studied, an individual in a local population can reproduce, die or migrate to neighboring sites. We prove that an increase of the death rate when the local population density is small (the Allee effect) may be critical for survival, and that the migration of large flocks of individuals is a possible solution to avoid extinction when the ...
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作者：Nagai, Hideo
作者单位：University of Osaka
摘要：We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon T in an incomplete market model, and then study the asymptotic behavior of minimizing probability as T -> infinity. This problem can be closely related to an ergodic risk-sensitive stochastic control problem in the risk-averse case. Indeed, in our main theorem, we relate the former problem concerning the asymptotics for risk minimization to the latter as its dual. As a result...
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作者：Gupta, Ankit
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Cell polarity refers to the spatial asymmetry of molecules on the cell membrane. Altschuler, Angenent, Wang and Wu have proposed a stochastic model for studying the emergence of polarity in the presence of feedback between molecules. We analyze their model further by representing it as a model of an evolving population with interacting individuals. Under a suitable scaling of parameters, we show that in the infinite population limit we get a Fleming-Viot process. Using well-known results for s...
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作者：Litvak, Nelly; Robert, Philippe
作者单位：University of Twente
摘要：If (C-n) is a Markov chain on a discrete state space S, a Markov chain (C-n, M-n) on the product space S x S, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain behaves like the original Markov chain and the second component changes only when both coordinates are equal. The asymptotic properties of this Markov chain are investigated. A representation of its invariant measure is, in particular, obtained. When the state space is infinite it is shown that th...
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作者：Jenkins, Paul A.; Song, Yun S.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to make progress on this problem. Specifically, closed-form expressions have been derived for the first few terms in an asymptotic expansion of the two-locus sampling distribution when the recombination rate p is moderate to large. In this paper, a new computa...
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作者：Lanchier, Nicolas
作者单位：Arizona State University; Arizona State University-Tempe
摘要：This article is concerned with the Axelrod model, a stochastic process which similarly to the voter model includes social influence, but unlike the voter model also accounts for homophily. Each vertex of the network of interactions is characterized by a set of F cultural features, each of which can assume q states. Pairs of adjacent vertices interact at a rate proportional to the number of features they share, which results in the interacting pair having one more cultural feature in common. Th...
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作者：Decreusefond, Laurent; Dhersin, Jean-Stephane; Moyal, Pascal; Viet Chi Tran
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; IMT Atlantique; Centre National de la Recherche Scientifique (CNRS); Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Technologie de Compiegne; Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
摘要：We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The l...
