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作者：Agazzi, Andrea; Dembo, Amir; Eckmann, Jean-Pierre
作者单位：Stanford University; Stanford University; University of Geneva; University of Geneva; University of Geneva; Duke University
摘要：We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it, we further establish the corresponding Wentzell-Freidlin (W-F) (infinite time horizon) asymptotic theory. These results apply to jump Markov processes that model the dynamics of chemical reaction networks under mass action kinetics, on a microscopic scale. We provide natural sufficient topological conditions for the applicabilit...
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作者：Gravner, Janko; Lyu, Hanbaek; Sivakoff, David
作者单位：University of California System; University of California Davis; University System of Ohio; Ohio State University
摘要：Fix a simple graph G = (V, E) and choose a random initial 3-coloring of vertices drawn from a uniform product measure. The 3-color cycle cellular automaton is a process in which at each discrete time step in parallel, every vertex with color i advances to the successor color (i + 1) mod 3 if in contact with a neighbor with the successor color, and otherwise retains the same color. In the Greenberg-Hastings model, the same update rule applies only to color 0, while other two colors automaticall...
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作者：Owada, Takashi
作者单位：Purdue University System; Purdue University
摘要：We investigate the topological dynamics of extreme sample clouds generated by a heavy tail distribution on R-d by establishing various limit theorems for Betti numbers, a basic quantifier of algebraic topology. It then turns out that the growth rate of the Betti numbers and the properties of the limiting processes all depend on the distance of the region of interest from the weak core, that is, the area in which random points are placed sufficiently densely to connect with one another. If the ...
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作者：Bandini, Elena; Cosso, Andrea; Fuhrman, Marco; Huyen Pham
作者单位：Luiss Guido Carli University; Polytechnic University of Milan; University of Milan; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Luiss Guido Carli University
摘要：We introduce a suitable backward stochastic differential equation (BSDE) to represent the value of an optimal control problem with partial observation for a controlled stochastic equation driven by Brownian motion. Our model is general enough to include cases with latent factors in mathematical finance. By a standard reformulation based on the reference probability method, it also includes the classical model where the observation process is affected by a Brownian motion (even in presence of a...
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作者：Pages, Gilles; Panloup, Fabien
作者单位：Sorbonne Universite; Universite d'Angers
摘要：We investigate a weighted multilevel Richardson-Romberg extrapolation for the ergodic approximation of invariant distributions of diffusions adapted from the one introduced in [Bernoulli 23 (2017) 2643-2692] for regular Monte Carlo simulation. In a first result, we prove under weak confluence assumptions on the diffusion, that for any integer R >= 2, the procedure allows us to attain a rate n(R/2R+1) whereas the original algorithm convergence is at a weak rate n(1/3). Furthermore, this is achi...
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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...
