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作者：Ivanovs, Jevgenijs
作者单位：Aarhus University
摘要：Let M and iota be the supremum and its time of a Levy process X on some finite time interval. It is shown that zooming in on X at its supremum, that is, considering ((X tau+t epsilon - M)/a epsilon)(t is an element of R) as e down arrow 0, results in (xi(t))(t is an element of R) constructed from two independent processes having the laws of some self-similar Levy process (X) over cap conditioned to stay positive and negative. This holds when X is in the domain of attraction of (X) over cap und...
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作者：Lipshutz, David; Ramanan, Kavita
作者单位：Brown University
摘要：The study of both sensitivity analysis and differentiability of the stochastic flow of a reflected process in a convex polyhedral domain is challenging due to the abrupt change in the nature of the dynamics at the boundary and is further complicated because the boundary is not smooth. These difficulties can be addressed by studying directional derivatives of an associated extended Skorokhod map, which is a deterministic mapping that takes an unconstrained path to a suitably reflected or constr...
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作者：Hoze, Nathanael; Holcman, David
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Cambridge; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention especially in stochastic analysis and statistical physics of cellular biology, as novel experimental data are now available, but their interpretation remains challenging. We derive here probability distribution functions for clusters that can either aggregate upon b...
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作者：Aghajani, Reza; Robert, Philippe; Sun, Wen
作者单位：University of California System; University of California San Diego
摘要：The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all copies of files stored on it are lost. In this way, repeated failures may lead to losses of files. The efficiency of such a network is directly related to the performances of the mechanism used to duplicate files on servers. In this paper, we study the evolution ...
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作者：Berestycki, Nathanael; Zhao, Lee Zhuo
作者单位：University of Cambridge
摘要：We introduce particle systems in one or more dimensions in which particles perform branching Brownian motion and the population size is kept constant equal to N > 1, through the following selection mechanism: at all times only the N fittest particles survive, while all the other particles are removed. Fitness is measured with respect to some given score function s : R-d -> R. For some choices of the function s, it is proved that the cloud of particles travels at positive speed in some possibly...
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作者：Chen, Yue; Busic, Ana; Meyn, Sean
作者单位：State University System of Florida; University of Florida; Inria; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Consider a stochastic process X on a finite state space X = {1,...,}d. It is conditionally Markov, given a real-valued input process sigma.0 This is assumed to be small, which is modeled through the scaling, sigma(t) = epsilon sigma(1)(t), 0 <= epsilon <= 1, where sigma(1) is a bounded stationary process. The following conclusions are obtained, subject to smoothness assumptions on the controlled transition matrix and a mixing condition on sigma : (i) A stationary version of the process is cons...
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作者：Pichler, Georg; Piantanida, Pablo; Matz, Gerald
作者单位：Technische Universitat Wien; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Let (X, Y) denote n independent, identically distributed copies of two arbitrarily correlated Rademacher random variables (X, Y). We prove that the inequality I( f (X); g (Y)) <= I(X; Y) holds for any two Boolean functions: f, g: {-1,1}(n) -> {-1,1} [I(.;.) denotes mutual information]. We further show that equality in general is achieved only by the dictator functions f(x) = +/- g(x) = +/- x(i), i is an element of {1,2,...,n}.
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作者：Deaconu, Madalina; Herrmann, Samuel
作者单位：Inria; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Bourgogne Europe; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The initial-boundary value problem for the heat equation is solved by using an algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to solve the Dirichlet problem for Laplace's equation, its implementation is rather easy. The construction of this algorithm can be considered as a natural consequence of previous works the authors completed on the hitting time approximation for Bessel processes and B...
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作者：Briand, Philippe; Elie, Romuald; Hu, Ying
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Savoie Mont Blanc; CNRS - National Institute for Mathematical Sciences (INSMI); CNRS - Institute of Physics (INP); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Gustave-Eiffel; Inria; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we study a new type of BSDE, where the distribution of the Y-component of the solution is required to satisfy an additional constraint, written in terms of the expectation of a loss function. This constraint is imposed at any deterministic time t and is typically weaker than the classical pointwise one associated to reflected BSDEs. Focusing on solutions (Y, Z, K) with deterministic K, we obtain the well-posedness of such equation, in the presence of a natural Skorokhod-type con...
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作者：Ye, Heng-Qing; Yao, David D.
作者单位：Hong Kong Polytechnic University; Columbia University
摘要：Multiclass queueing networks (MQN) are, in general, difficult objects to study analytically. The diffusion approximation refers to using the stationary distribution of the diffusion limit as an approximation of the diffusion-scaled process (say, the workload) in the original MQN. To validate such an approximation amounts to justifying the interchange of two limits, t -> infinity and k -> infinity, with t being the time index and k, the scaling parameter. Here, we show this interchange of limit...
