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作者：Jaber, Eduardo Abi; Larsson, Martin; Pulido, Sergio
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Swiss Federal Institutes of Technology Domain; ETH Zurich; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE); Universite Paris Saclay; 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; ENSTA Paris; Ecole Polytechnique; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are neither semimartingales, nor Markov processes in general. We provide explicit exponential-affine representations of the Fourier-Laplace functional in terms of the solution of an associated system of deterministic integral equations of convolution type, extending well-known form...
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作者：Guo, Gaoyue; Obloj, Jan
作者单位：University of Oxford
摘要：We develop computational methods for solving the martingale optimal transport (MOT) problem-a version of the classical optimal transport with an additional martingale constraint on the transport's dynamics. We prove that a general, multi-step multi-dimensional, MOT problem can be approximated through a sequence of linear programming (LP) problems which result from a discretization of the marginal distributions combined with an appropriate relaxation of the martingale condition. Further, we est...
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作者：Diehl, Christina S.; Kersting, Goetz
作者单位：Goethe University Frankfurt
摘要：We study tree lengths in Lambda-coalescents without a dust component from a sample of n individuals. For the total length of all branches and the total length of all external branches, we present laws of large numbers in full generality. The other results treat regularly varying coalescents with exponent 1, which cover the Bolthausen-Sznitman coalescent. The theorems contain laws of large numbers for the total length of all internal branches and of internal branches of order a (i.e., branches ...
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作者：Gorham, Jackson; Duncan, Andrew B.; Vollmer, Sebastian J.; Mackey, Lester
作者单位：Stanford University; Imperial College London; University of Warwick; Microsoft
摘要：Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds are readily available for a diversity of univariate targets, few multivariate targets have been analyzed. We introduce a new class of characterizing operators based on Ito diffusions and develop explicit multivariate Stein factor bounds for any target with a f...
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作者：Sankararaman, Abishek; Baccelli, Francois; Foss, Sergey
作者单位：University of Texas System; University of Texas Austin; Heriot Watt University; Novosibirsk State University; Russian Academy of Sciences; Sobolev Institute of Mathematics
摘要：Consider a countably infinite collection of interacting queues, with a queue located at each point of the d-dimensional integer grid, having independent Poisson arrivals, but dependent service rates. The service discipline is of the processor sharing type, with the service rate in each queue slowed down, when the neighboring queues have a larger workload. The interactions are translation invariant in space and is neither of the Jackson Networks type, nor of the mean-field type. Coupling and pe...
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作者：Champagnat, Nicolas; Henry, Benoit
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; IMT - Institut Mines-Telecom; Universite de Lille; IMT Nord Europe
摘要：This work is devoted to the study of scaling limits in small mutations and large time of the solutions u(epsilon) of two deterministic models of phenotypic adaptation, where the parameter epsilon > 0 scales the size or frequency of mutations. The second model is the so-called Lotka-Volterra parabolic PDE in Rd with an arbitrary number of resources and the first one is a version of the second model with finite phenotype space. The solutions of such systems typically concentrate as Dirac masses ...
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作者：Degond, P.; Pulvirenti, M.
作者单位：Imperial College London; University of L'Aquila
摘要：We consider a N-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit N -> infinity, as following from the previous analysis in (J. Stat. Phys. 163 (2016) 41-60) can be rigorously derived. This means that the statistical independence (propagation of chaos) is indeed recovered in the limit, provided it is assumed at time zero.
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作者：Budhiraja, Amarjit; Mukherjee, Debankur; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University; University of Michigan System; University of Michigan
摘要：We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson processes with rate lambda, and each task is irrevocably assigned to the shortest queue among the one it first appears and its d - 1 randomly selected neighbors. This model has been extensively studied when...
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作者：Jin, Ke
作者单位：University of Delaware
摘要：The Mallows measure is a probability measure on S-n where the probability of a permutation pi is proportional to q(l(pi)) with q > 0 being a parameter and l(pi) the number of inversions in pi. We prove a weak law of large numbers for the length of the longest common subsequences of two independent permutations drawn from the Mallows measure, when q is a function of n and n(1 - q) has limit in R as n ->infinity.
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作者：Burdzy, Krzysztof; Gauthier, Carl-Erik
作者单位：University of Washington; University of Washington Seattle
摘要：We consider random reflections (according to the Lambertian distribution) of a light ray in a thin variable width (but almost circular) tube. As the width of the tube goes to zero, properly rescaled angular component of the light ray position converges in distribution to a diffusion whose parameters (diffusivity and drift) are given explicitly in terms of the tube width.
