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作者：Rassoul-Agha, F
作者单位：University System of Ohio; Ohio State University
摘要：The point of view of the particle is an approach that has proven very powerful in the study of many models of random motions in random media. We provide a new use of this approach to prove the law of large numbers in the case of one or higher-dimensional, finite range, transient random walks in mixing random environments. One of the advantages of this method over what has been used so far is that it is not restricted to i.i.d. environments.
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作者：Talagrand, M
作者单位：Sorbonne Universite
摘要：Physicists have studied the stochastic assignment problem using ideas from statistical mechanics. For a version of this problem, we give, at high enough temperature, a complete proof of the existence of the structure they predict.
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作者：Grigor'yan, A; Kelbert, M
作者单位：Imperial College London; Swansea University; Russian Academy of Sciences; Institute of Earthquake Prediction Theory & Mathematical Geophysics
摘要：We relate the recurrence and transience of a branching diffusion process on a Riemannian manifold M to some properties of a linear elliptic operator on M (including spectral properties). There is a trade-off between the tendency of the transient Brownian motion to escape and the birth process of the new particles. If the latter has a high enough intensity then it may override the transience of the Brownian motion, leading to the recurrence of the branching process, and vice versa. In the case ...
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作者：Duan, JQ; Lu, KN; Schmalfuss, B
作者单位：Illinois Institute of Technology; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Brigham Young University; Michigan State University
摘要：Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite- and infinite-dimensional autonomous deterministic systems and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant manifolds for infinite-dimensional random dynamical systems generated by stochastic partial differential equations. We first introduce a random...
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作者：Karatzas, I; Zikovic, G
作者单位：Columbia University; Columbia University
摘要：We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of asymptotic elasticity of Kramkov and Schachermayer is extended to the time-dependent case. By imposing no smoothness requirements on the utility function in the temporal argument, we can treat both pure consumption and combined consump...
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作者：Meester, R; Znamenski, D
作者单位：Vrije Universiteit Amsterdam
摘要：One of the key problems related to the Bak-Sneppen evolution model on the circle is computing the limit distribution of the fitness at a fixed observation vertex in the stationary regime as the size of the system tends to infinity. Some simulations have suggested that this limit distribution is uniform on (f, 1) for some f similar to 2/3. In this article, we prove that the mean of the fitness in the stationary regime is bounded away from 1, uniformly in the size of the system, thereby establis...
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作者：Panchenko, D
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We introduce a symmetrization technique that allows us to translate a problem of controlling the deviation of some functionals on a product space from their mean into a problem of controlling the deviation between two independent copies of the functional. As an application we give a new easy proof of Talagrand's concentration inequality for empirical processes, where besides symmetrization we use only Talagrand's concentration inequality on the discrete cube {0, 1}(n). As another application o...
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作者：Fernique, X
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：Let G be a Gaussian vector taking its values in a separable Frechet space E. We denote by gamma its law and by (H, parallel to(.)parallel to) its reproducing Hilbert space. Moreover, let X be an E-valued random vector of law mu. In the first section, we prove that if mu is absolutely continuous relative to gamma, then there exist necessarily a Gaussian vector G' of law gamma and an H-valued random vector Z such that G' + Z has the law mu of X. This fact is a direct consequence of concentration...
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作者：Durrett, R; Limic, V
作者单位：Cornell University; University of British Columbia
摘要：Motivated by the problem of the evolution of DNA sequences, Kauffman and Levin introduced a model in which fitnesses were assigned to strings of 0's and 1's of length N based on the values observed in a sliding window of length K + 1. When K greater than or equal to 1, the landscape is quite complicated with many local maxima. Its properties have been extensively investigated by simulation but until our work and the independent investigations of Evans and Steinsaltz little was known rigorously...
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作者：Keane, M; Steif, JE
作者单位：Wesleyan University; University of Amsterdam; Chalmers University of Technology; University System of Georgia; Georgia Institute of Technology
摘要：We show that there is a finitary isomorphism from a finite state independent and identically distributed (i.i.d.) process to the T, T-1 process associated to one-dimensional random walk with positive drift. This contrasts with the situation for simple symmetric random walk in any dimension, where it cannot be a finitary factor of any i.i.d. process, including in d greater than or equal to 5, where it becomes weak Bernoulli.
