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作者：Kabluchko, Zakhar
作者单位：Ulm University
摘要：We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to infinity. The random fields considered include costs of assignments. weights of Hamiltonian cycles and spanning trees, energies of directed polymers, locations of particles in the branching random walk, as well as energies in the Sherrington-Kirkpatrick and Edwards-Anderson models. The distribution of levels ...
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作者：Nutz, Marcel
作者单位：Columbia University
摘要：We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in terms of the opportunity process, which is characterized as the minimal solution of the Bellman equation. We also give verification theorems for this equation.
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作者：Adler, Robert J.; Blanchet, Jose H.; Liu, Jingchen
作者单位：Technion Israel Institute of Technology; Columbia University; Columbia University
摘要：Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of excursions above high levels, b. Naive Monte Carlo takes an exponential, in b, computational cost to estimate these probabilities and conditional expectations for a prescribed relative accuracy. In contrast, our Monte Carlo procedures achieve, at worst, polynom...
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作者：Tong, Xin Thomson; van Handel, Ramon
作者单位：Princeton University
摘要：We consider a bivariate stationary Markov chain (X-n, Y-n)(n >= 0) in a Polish state space, where only the process (Y-n)(n >= 0) is presumed to be observable. The goal of this paper is to investigate the ergodic theory and stability properties of the measure-valued process (Pi(n))(n >= 0), where Pi(n) is the conditional distribution of X-n given Y-0, ... ,Y-n. We show that the ergodic and stability properties of (Pi(n))(n >= 0) are inherited from the ergodicity of the unobserved process (X-n)(...
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作者：Janson, Svante; Luczak, Tomasz; Turova, Tatyana; Vallier, Thomas
作者单位：Uppsala University; Adam Mickiewicz University; Lund University; University of Helsinki
摘要：Bootstrap percolation on the random graph C-n,C-p is a process of spread of activation on a given realization of the graph with a given number of initially active nodes. At each step those vertices which have not been active but have at least r >= 2 active neighbors become active as well. We study the size A* of the final active set. The parameters of the model are, besides r (fixed) and n (tending to infinity), the size a = a(n) of the initially active set and the probability p = p(n) of the ...
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作者：Addario-Berry, Louigi; Griffiths, Simon; Kang, Ross J.
作者单位：McGill University; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Durham University
摘要：We study invasion percolation on Aldous' Poisson-weighted infinite tree, and derive two distinct Markovian representations of the resulting process. One of these is the sigma -> infinity limit of a representation discovered by Angel et al. [Ann. Appl. Probab. 36 (2008) 420-466]. We also introduce an exploration process of a randomly weighted Poisson incipient infinite cluster. The dynamics of the new process are much more straightforward to describe than those of invasion percolation, but it t...
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作者：Chassagneux, Jean-Francois; Elie, Romuald; Kharroubi, Idris
作者单位：Universite Paris Saclay; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we study the discrete-time approximation of multidimensional reflected BSDEs of the type of those presented by Hu and Tang [Probab. Theory Related Fields 147 (2010) 89-121] and generalized by Hamadene and Zhang [Stochastic Process. Appl. 120 (2010) 403-426]. In comparison to the penalizing approach followed by Hamadene and Jeanblanc [Math. Oper Res. 32 (2007) 182-192] or Elie and Kharroubi [Statist. Probab. Lett. 80 (2010) 1388-1396], we study a more natural scheme based on obli...
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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：Kardaras, Constantinos; Robertson, Scott
作者单位：Boston University; Carnegie Mellon University
摘要：This paper addresses the question of how to invest in a robust growth-optimal way in a market where the instantaneous expected return of the underlying process is unknown. The optimal investment strategy is identified using a generalized version of the principal eigenfunction for an elliptic second-order differential operator, which depends on the covariance structure of the underlying process used for investing. The robust growth-optimal strategy can also be seen as a limit, as the terminal d...
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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...
