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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.
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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.
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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 >...
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作者：Clement, Emmanuelle; Kohatsu-Higa, Arturo; Lamberton, Damien
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University of Osaka
摘要：In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach considered here uses the properties of the linear equation satisfied by the error process. This methodology seems to apply to a large class of processes and we present as an example the weak approximation of stochastic delay equations.
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作者：Hayes, Thomas P.; Vigoda, Eric
作者单位：University of California System; University of California Berkeley; University System of Georgia; Georgia Institute of Technology
摘要：We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the stationary distribution to avoid worst-case configurations which arise in the traditional approach. As an application, we show that for k/Delta > 1.764, the Glauber dynamics on k-colorings of a graph on n vertices with maximum degree Delta converges in O (n log n) s...
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作者：Harrison, J. Michael
作者单位：Stanford University
摘要：Due to a printing error the above mentioned article had numerous equations appearing incorrectly in the print version of this paper. The entire article follows as it should have appeared. IMS apologizes to the author and the readers for this error. A recent paper by Harrison and Van Mieghem explained in general mathematical terms how one forms an equivalent workload formulation of a Brownian network model. Denoting by Z(t) the state vector of the original Brownian network, one has a lower dime...
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作者：Mokkadem, Abdelkader; Pelletier, Mariane
作者单位：Universite Paris Saclay
摘要：The first aim of this paper is to establish the weak convergence rate of nonlinear two-time-scale stochastic approximation algorithms. Its second aim is to introduce the averaging principle in the context of two-time-scale stochastic approximation algorithms. We first define the notion of asymptotic efficiency in this framework, then introduce the averaged two-time-scale stochastic approximation algorithm, and finally establish its weak convergence rate. We show, in particular, that both compo...
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作者：Rheinlaender, Thorsten; Steiger, Gallus
作者单位：University of London; London School Economics & Political Science; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We determine the minimal entropy martingale measure for a general class of stochastic volatility models where both price process and volatility process contain jump terms which are correlated. This generalizes previous studies which have treated either the geometric Levy case or continuous price processes with an orthogonal volatility process. We proceed by linking the entropy measure to a certain semi-linear integro-PDE for which we prove the existence of a classical solution.
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作者：Wuethrich, Mario V.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We define a heteropolymer in a medium with random droplets. We prove that for this model we have two regimes: a delocalized one and a localized one. In the localized regime we prove tightness to the droplets, whereas in the delocalized regime we prove diffusive path behavior.
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作者：Andjel, E. D.; Menshikov, M. V.; Sisko, V. V.
作者单位：Aix-Marseille Universite; Durham University; Universidade de Sao Paulo
摘要：We show that certain Markov jump processes associated to crystal growth models are positive recurrent when the parameters satisfy a rather C natural condition.
