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作者：Hermon, Jonathan; Salez, Justin
作者单位：University of Cambridge; Universite Paris Cite
摘要：We show that the spectral gap of a general zero range process can be controlled in terms of the spectral gap for a single particle. This is in the spirit of Aldous' famous spectral-gap conjecture for the interchange process, now resolved by Caputo et al. Our main inequality decouples the role of the geometry (defined by the jump matrix) from that of the kinetics (specified by the exit rates). Among other consequences, the various spectral gap estimates that were so far only available on the co...
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作者：Sun, Rongfeng; Swart, Jan M.; Yu, Jinjiong
作者单位：National University of Singapore; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; New York University; NYU Shanghai
摘要：A one-dimensional interacting particle system is said to exhibit interface tightness if starting in an initial condition describing the interface between two constant configurations of different types, the process modulo translations is positive recurrent. In a biological setting, this describes two populations that do not mix, and it is believed to be a common phenomenon in one-dimensional particle systems. Interface tightness has been proved for voter models satisfying a finite second moment...
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作者：Lachieze-Rey, Raphael; Schulte, Matthias; Yukich, J. E.
作者单位：Universite Paris Cite; University of Bern; Lehigh University
摘要：We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance for a large class of geometric functionals of marked Poisson and binomial point processes on general metric spaces. The rates are valid whenever the geometric functional is expressible as a sum of exponentially stabilizing score functions satisfying a moment condition. By incorporating stabilization methods into the Malliavin-Stein theory, we obtain rates of normal approximation for sums of stab...
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作者：Crisan, Dan; McMurray, Eamon
作者单位：Imperial College London
摘要：We present two cubature on Wiener space algorithms for the numerical solution of McKean-Vlasov SDEs with smooth scalar interaction. First, we consider a method introduced in [Stochastic Process. Appl. 125 (2015) 2206-2255] under a uniformly elliptic assumption and extend the analysis to a uniform strong Hormander assumption. Then we introduce a new method based on Lagrange polynomial interpolation. The analysis hinges on sharp gradient to time-inhomogeneous parabolic PDEs bounds. These bounds ...
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作者：Figueroa-Lopez, Jose E.; Olafsson, Sveinn
作者单位：Washington University (WUSTL); University of California System; University of California Santa Barbara
摘要：Since the work of Page in the 1950s, the problem of detecting an abrupt change in the distribution of stochastic processes has received a great deal of attention. In particular, a deep connection has been established between Lorden's minimax approach to change-point detection and the widely used CUSUM procedure, first for discrete-time processes, and subsequently for some of their continuous-time counterparts. However, results for processes with jumps are still scarce, while the practical impo...
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作者：Gracar, Peter; Stauffer, Alexandre
作者单位：University of Cologne; University of Bath
摘要：Consider the graph induced by Z(d), equipped with uniformly elliptic random conductances. At time 0, place a Poisson point process of particles on Z(d) and let them perform independent simple random walks. Tessellate the graph into cubes indexed by i is an element of Z(d) and tessellate time into intervals indexed by tau. Given a local event E(i, tau) that depends only on the particles inside the space time region given by the cube i and the time interval tau, we prove the existence of a Lipsc...
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作者：Lachieze-Rey, Raphael
作者单位：Universite Paris Cite
摘要：This article presents a complete second-order theory for a large class of geometric functionals on homogeneous Poisson input. In particular, the results do not require the existence of a radius of stabilisation. Hence they can be applied to geometric functionals of spatial shot-noise fields excursions such as volume, perimeter, or Euler characteristic (the method still applies to stabilising functionals). More generally, it must be checked that a local contribution to the functional is not str...
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作者：Liu, Yanghui; Tindel, Samy
作者单位：Purdue University System; Purdue University
摘要：In this article, we consider the so-called modified Euler scheme for stochastic differential equations (SDEs) driven by fractional Brownian motions (fBm) with Hurst parameter 1/3 < H < 1/2. This is a first-order time-discrete numerical approximation scheme, and has been introduced in [Ann. Appl. Probab. 26 (2016) 1147-1207] recently in order to generalize the classical Euler scheme for Ito SDEs to the case H > 1/2. The current contribution generalizes the modified Euler scheme to the rough cas...
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作者：Atar, Rami; Cohen, Asaf
作者单位：Technion Israel Institute of Technology; University of Haifa
摘要：We study a single-server Markovian queueing model with N customer classes in which priority is given to the shortest queue. Under a critical load condition, we establish the diffusion limit of the nominal workload and queue length processes in the form of a Walsh Brownian motion (WBM) living in the union of the N nonnegative coordinate axes in R-N and a linear transformation thereof. This reveals the following asymptotic behavior. Each time that queues begin to build starting from an empty sys...
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作者：Schlichting, Andre; Slowik, Martin
作者单位：University of Bonn; Technical University of Berlin
摘要：We investigate the metastable behavior of reversible Markov chains on possibly countable infinite state spaces. Based on a new definition of metastable Markov processes, we compute precisely the mean transition time between metastable sets. Under additional size and regularity properties of metastable sets, we establish asymptotic sharp estimates on the Poincare and logarithmic Sobolev constant. The main ingredient in the proof is a capacitary inequality along the lines of V. Maz'ya that relat...
