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作者：Burdzy, Krzysztof; Tadic, Tvrtko
作者单位：University of Washington; University of Washington Seattle; Microsoft; University of Zagreb
摘要：We consider two-dimensional and three-dimensional semi-infinite tubes made of Lambertian material, so that the distribution of the direction of a reflected light ray has the density proportional to the cosine of the angle with the normal vector. If the light source is far away from the opening of the tube then the exiting rays are (approximately) collimated in two dimensions but are not collimated in three dimensions. An observer looking into the three-dimensional tube will see infinitely brig...
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作者：Chen, Zhen-Qing; Fan, Wai-Tong (Louis)
作者单位：University of Washington; University of Washington Seattle; University of Wisconsin System; University of Wisconsin Madison
摘要：A new non-conservative stochastic reaction diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. We show that in the macroscopic limit, the particle densities converge to the solution of a coupled nonlinear heat equations. For this, w...
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作者：Helmes, Kurt L.; Stockbridge, Richard H.; Zhu, Chao
作者单位：Humboldt University of Berlin; University of Wisconsin System; University of Wisconsin Milwaukee
摘要：This paper establishes conditions for optimality of an (s, S) ordering policy for the minimization of the long-term average cost of one-dimensional diffusion inventory models. The class of such models under consideration have general drift and diffusion coefficients and boundary points that are consistent with the notion that demand should tend to reduce the inventory level. Characterization of the cost of a general (s, S) policy as a function F of two variables naturally leads to a nonlinear ...
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作者：Ball, Frank; Neal, Peter
作者单位：University of Nottingham; Lancaster University
摘要：For a supercritical configuration model random graph, it is well known that, subject to mild conditions, there exists a unique giant component, whose size R-n is O (n), where n is the total number of vertices in the random graph. Moreover, there exists 0 < rho <= 1 such that R-n/n ->(p) rho as n -> infinity. We show that for a sequence of well behaved configuration model random graphs with a deterministic degree sequence satisfying 0 < rho < 1; there exists sigma(2) > 0, such that var(root n(R...
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作者：Mourrat, Jean-Christophe; Nolen, James
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); Duke University
摘要：In the homogenization of divergence-form equations with random coefficients, a central role is played by the corrector. We focus on a discrete space setting and on dimension 3 and more. Under a minor smoothness assumption on the law of the random coefficients, we identify the scaling limit of the corrector, which is akin to a Gaussian free field. This completes the argument started in [Ann. Probab. 44 (2016) 3207-3233].
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作者：Pillai, Natesh S.; Smith, Aaron
作者单位：Harvard University; University of Ottawa
摘要：Determining the mixing time of Kac's random walk on the sphere Sn-1 is a long-standing open problem. We show that the total variation mixing time of Kac's walk on Sn-1 is between 1/2n log(n) and 200n log(n) for all n sufficiently large. Our bound is thus optimal up to a constant factor, improving on the best-known upper bound of O(n(5) log(n)(2)) due to Jiang [Ann. AppL Probab. 22 (2012) 1712-1727]. Our main tool is a non-Markovian coupling recently introduced by the second author in [Ann. App...
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作者：De Angelis, Tiziano; Ekstrom, Erik
作者单位：University of Leeds; Uppsala University
摘要：We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obtained by establishing for the first time a new connection between singular control problems with an absorbing boundary and optimal stopping problems on a diffusion reflected at 0...
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作者：Lux, Thibaut; Papapantoleon, Antonis
作者单位：Technical University of Berlin
摘要：We derive upper and lower bounds on the expectation of f (S) under dependence uncertainty, that is, when the marginal distributions of the random vector S = (S-1,..., S-d) are known but their dependence structure is partially unknown. We solve the problem by providing improved Frechet-Hoeffding bounds on the copula of S that account for additional information. In particular, we derive bounds when the values of the copula are given on a compact subset of [0, 1](d), the value of a functional of ...
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作者：Pistorius, Martijn; Stadje, Mitja
作者单位：Imperial College London; Ulm University
摘要：In this paper, we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency, we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition, dynamic deviation measures are characterised as the solutions to a certain class of stochastic differential equations. We establish for any dynamic deviation measure an integr...
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作者：Bovier, Anton; Hartung, Lisa
作者单位：University of Bonn; New York University; University of Bonn
摘要：We extend the results of Arguin et al. [Probab. Theory Related Fields 157 (2013) 535-574] and Aidekon et al. [Probab. Theory Related Fields 157 (2013) 405-451] on the convergence of the extremal process of branching Brownian motion by adding an extra dimension that encodes the location of the particle in the underlying Galton-Watson tree. We show that the limit is a cluster point process on R+ x R where each cluster is the atom of a Poisson point process on R+ x R with a random intensity measu...
