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作者：Vasdekis, G.; Roberts, G. O.
作者单位：University of London; University College London; University of Warwick
摘要：The Zig-Zag process is a piecewise deterministic Markov process, efficiently used for simulation in an MCMC setting. As we show in this article, it fails to be exponentially ergodic on heavy tailed target distributions. We introduce an extension of the Zig-Zag process by allowing the process to move with a nonconstant speed function s, depending on the current state of the process. We call this process Speed Up Zig-Zag (SUZZ). We provide conditions that guarantee stability properties for the S...
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作者：Guo, Shuchen; Luo, Dejun
作者单位：Chinese Academy of Sciences
摘要：We consider moderately interacting particle systems with singular inter-action kernel and environmental noise. It is shown that the mollified empirical measures converge in strong norms to the unique (local) solutions of nonlin-ear Fokker-Planck equations. The approach works for the Biot-Savart and repulsive Poisson kernels.
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作者：Gantert, Nina; Nestoridi, Evita; Schmid, Dominik
作者单位：Technical University of Munich; Princeton University
摘要：We study mixing times of the symmetric and asymmetric simple exclu-sion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on the entering and exiting rates as well as on the rates in the bulk, and show that the pro-cess exhibits pre-cutoff and in some cases cutoff. Our main contribution is to study mixing times for the asymmetric simple exclusion process with open boundaries. We show that the order of the mixing time ...
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作者：Jahnel, Benedikt; Koeppl, Jonas
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider irreversible translation-invariant interacting particle systems on the d-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification we prove that zero relative entropy loss of a translation-invariant measure implies that the measure is Gibbs w.r.t. the same specification as the time-stationary Gibbs measure. As an application, we obtain the att...
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作者：Kasprzak, Mikolaj J.; Peccati, Giovanni
作者单位：University of Luxembourg
摘要：We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions, holding in every dimension. Such a finding constitutes a substantial extension of the one-dimensional bounds deduced in Chatterjee (Ann. Probab. 36 (2008) 1584-1610) and Lachieze-Rey and Peccati (Ann. Appl. Probab. 27 (2017) 1992-2031), as well as of the multidime...
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作者：Onaran, Efe; Bobrowski, Omer; Adler, Robert J.
作者单位：Technion Israel Institute of Technology; University of London; Queen Mary University London
摘要：We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in Rd. The dynamics we study here are those of a Markov birth-death process. We prove functional limit theorems in the so-called thermodynamic regime. Our results are applicable to several functionals of interest in the stochastic geometry literature, including subgraph and component counts in the random geometric graphs.
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作者：Tanana, Anastasiya
作者单位：University of Texas System; University of Texas Austin
摘要：In this paper, we study expected utility maximization under ratchet and drawdown constraints on consumption in a general incomplete semimartingale market using duality methods. The optimization is considered with respect to two parameters: the initial wealth and the essential lower bound on consumption process. In order to state the problem and define the primal do-mains, we introduce a natural extension of the notion of running maximum to arbitrary nonnegative optional processes and study its...
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作者：Djete, Mao Fabrice
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we provide convergence and existence results for mean field games of controls. Mean field games of controls are a class of mean field games where the mean field interactions are achieved through the joint (conditional) distribution of the controlled state and the control process. The framework we are considering allows to control the diffusion coefficient & sigma;, and the controls/strategies are supposed to be of open loop type. Using (con-trolled) Fokker-Planck equations, we i...
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作者：Erdos, Laszlo; Krueger, Torben; Enfrew, David
作者单位：University of Erlangen Nuremberg; State University of New York (SUNY) System; Binghamton University, SUNY
摘要：We consider the long time asymptotic behavior of a large system of N linear differential equations with random coefficients. We allow for general elliptic correlation structures among the coefficients, thus we substantially generalize our previous work (SIAM J. Math. Anal. 50 (2018) 3271-3290) that was restricted to the independent case. In particular, we analyze a recent model in the theory of neural networks (Phys. Rev. E 97 (2018) 062314) that specifically focused on the effect of the distr...
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作者：Bayer, Christian; Hager, Paul P.; Riedel, Sebastian; Schoenmakers, John
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; Fern University Hagen
摘要：We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the un-derlying stochastic process X. We consider classic and randomized stopping times represented by linear and nonlinear functionals of the rough path sig-nature X
