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作者：Grotto, Francesco; Luongo, Eliseo; Romito, Marco
作者单位：University of Pisa; Scuola Normale Superiore di Pisa
摘要：We consider a system of N point vortices in a bounded domain with null total circulation, whose statistics are given by the canonical Gibbs ensemble at inverse temperature beta >= 0. We prove that the space-time fluctuation field around the (constant) mean field limit satisfies when N -> infinity a generalized version of two-dimensional Euler dynamics preserving the Gaussian energyenstrophy ensemble.
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作者：Leao, Dorival; Ohashi, Alberto; DE Souza, Francys a.
作者单位：Universidade de Brasilia
摘要：In this article, we present a general methodology for stochastic control problems driven by the Brownian motion filtration including non-Markovian and nonsemimartingale state processes controlled by mutually singular measures. The main result of this paper is the development of a numerical scheme for computing near-optimal controls associated with controlled Wiener functionals via a finite-dimensional approximation procedure. The approach does not require functional differentiability assumptio...
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作者：Erhard, Dirk; Reis, Guilherme
作者单位：Universidade Federal da Bahia; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We introduce a simple but powerful strategy to study processes driven by two or more reinforcement mechanisms in competition. We apply our method to two types of models: to nonconservative zero range processes on finite graphs, and to multi-particle random walks with positive and negative reinforcement on the edges. The results hold for a broad class of reinforcement functions, including those with superlinear growth. Our strategy consists in a comparison of the original processes with suitabl...
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作者：Nachmias, Asaf; Tang, Pengfei
作者单位：Tel Aviv University; Tianjin University
摘要：We study the spectral and diffusive properties of the wired minimal span-ning forest (WMSF) on the Poisson-weighted infinite tree (PWIT). LetMbethe tree containing the root in the WMSF on the PWIT and(Y-n)(n >= 0)be asimple random walk onMstarting from the root. We show that almost surelyMhasP[Y-2n=Y-0]=n-(3/4+o(1))and dist(Y-0,Y-n)=n(1/4+o(1))with highprobability. That is, the spectral dimension ofMis 3/2 and its typical dis-placement exponent is 1/4, almost surely. These confirm Addario-Berr...
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作者：Liu, Yucheng
作者单位：University of British Columbia
摘要：Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On Z, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing...
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作者：Acciaio, Beatrice; Hou, Songyan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：nite discrete-time. We show that the adapted empirical measure introduced in in compact spaces can be defined analogously on Rd, and that it converges almost surely to the underlying measure under the adapted Wasserstein distance. Moreover, we quantitatively analyze the convergence of the adapted Wasserstein distance between those two measures. We establish convergence rates of the expected error as well as the deviation error under different moment conditions. Under suitable integrability and...
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作者：Poisat, Julien; Simenhaus, Francois
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We consider a one-dimensional simple random walk killed by quenched soft obstacles. The position of the obstacles is drawn according to a renewal process with a power-law increment distribution. In a previous work, we computed the large-time asymptotics of the quenched survival probability. In the present work we continue our study by describing the behaviour of the random walk conditioned to survive. We prove that with large probability, the walk quickly reaches a unique time-dependent optima...
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作者：Xu, Wei
作者单位：Beijing Institute of Technology
摘要：This paper is concerned with the evolution dynamics of local times ofa spectrally positive stable process in the spatial direction. The main resultsstate that conditioned on the finiteness of the first time at which the local timeat zero exceeds a given value, the local times at positive half line are equal indistribution to the unique solution of a stochastic Volterra equation driven bya Poisson random measure whose intensity coincides with the L & eacute;vy measure.This helps us to provide n...
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作者：Mathews, Joseph; Schmidler, Scott C.
作者单位：Duke University
摘要：We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global mixing of the Markov kernel is slow; in such cases our approach establishes the benefits of SMC over the corresponding Markov chain Monte Carlo (MCMC) estimator. The lack of global mixing is addressed by sequentially controlling the bias introduced by SMC r...
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作者：Talbi, Mehdi; Touzi, Nizar; Zhang, Jianfeng
作者单位：Universite Paris Cite; New York University; New York University Tandon School of Engineering; University of Southern California
摘要：This paper analyzes the convergence of the finite population optimal stopping problem towards the corresponding mean field limit. Building on the viscosity solution characterization of the mean field optimal stopping problem of our previous papers ( SIAM J. Control Optim. 61 (2023) 1712-1736, 2140-2164), we prove the convergence of the value functions by adapting the Barles-Souganidis ( Asymptot. Anal. 4 (1991) 271-283) monotone scheme method to our context. We next characterize the optimal st...
