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作者：Rutiten, Daan; Mukherjee, Debankur
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：The analysis of large-scale, parallel-server load balancing systems has relied heavily on mean-field analysis. A pivotal assumption for this framework is that servers are exchangeable. However, modern data-centers have data locality constraints, such that tasks of a particular type can only be routed to a small subset of servers. An emerging line of research, therefore, considers load balancing algorithms on bipartite graphs where vertices represent task types and servers, respectively. Due to...
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作者：Thuan, Nguyen tran
作者单位：Saarland University; Vinh University
摘要：This article investigates discrete-time approximations of stochastic integrals driven by semimartingales with jumps via weighted bounded mean osfor the approximation error depending on the weight, and it allows a change of the underlying measure which leaves the error estimates unchanged. To take advantage of this approach, we propose a new approximation scheme obtained from an adjustment for the Riemann approximation based on tracking jumps of the underlying semimartingale. We discuss a way t...
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作者：Chong, Carsten H.; Hoffmann, Marc; Liu, Yanghui; Rosenbaum, Mathieu; Szymanski, Gregoire
作者单位：Hong Kong University of Science & Technology; Universite PSL; Universite Paris-Dauphine; City University of New York (CUNY) System; Baruch College (CUNY); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter H < 0.5. In this paper, we derive a consistent and asymptotically mixed normal estimator of H based on high-frequency price observations. In contrast to previous works, we work in a semiparametric setting and do not assume any a p...
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作者：Hasenpflug, Mareike; Rudolf, Daniel; Sprungk, Bjoern
作者单位：University of Passau; Technical University Freiberg
摘要：For l : R-d -> [0,infinity) we consider the sequence of probability measures (mu(n))(n is an element of N), where mu(n) is determined by a density that is proportional to exp(-nl). We allow for infinitely many global minimal points of l, as long as they form a finite union of compact manifolds. In this scenario, we show estimates for the p-Wasserstein convergence of (mu(n))(n is an element of N) to its limit measure. Imposing regularity conditions we obtain a speed of convergence of n(-1/(2p))...
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作者：Wang, Haoyu
作者单位：Yale University
摘要：We prove the first explicit rate of convergence to the Tracy-Widom distribution for the fluctuation of the largest eigenvalue of sample covariance matrices that are not integrable. Our primary focus is matrices of type X*X and the proof follows the Erdos-Schlein-Yau dynamical method. We use a recent approach to the analysis of the Dyson Brownian motion from (J. Eur. Math. Soc. (JEMS) 24 (2022) 2823-2873) to obtain a quantitative error estimate for the local relaxation flow at the edge. Togethe...
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作者：Cass, Thomas; Lyons, Terry; Xu, Xingcheng
作者单位：Imperial College London; University of Oxford
摘要：Suppose that gamma and sigma are two continuous bounded variation paths, which take values in a finite-dimensional inner product space V. The recent papers (J. Mach. Learn. Res. 20 (2019) 1-45) and (SIAM J. Math. Data Sci. 3 (2021) 873-899), respectively, introduced the truncated and the untruncated signature kernel of gamma and sigma, and showed how these concepts can be used in classification and prediction tasks involving multivariate time series. In this paper, we introduce signature kerne...
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作者：Feldheim, Ohad Noy; Gurel-Gurevich, Ori; Li, Jiange
作者单位：Hebrew University of Jerusalem; Harbin Institute of Technology
摘要：In the two-thinning balls-and-bins model, an overseer is provided with uniform random allocation of m balls into n bins in an on-line fashion. The overseer may reject the allocation of each ball, in which case it is placed into a new bin, drawn independently, uniformly at random. The purpose of the overseer is to reduce the maximum load, that is, the difference between the maximum number of balls in a single bin and the average number of balls among all bins. We provide tight estimates for thr...
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作者：Goldenshluger, Alexander; Jacobovic, Royi
作者单位：University of Haifa
摘要：Suppose that particles are randomly distributed in R-d, and they are subject to identical stochastic motion independently of each other. The Smoluchowski process describes fluctuations of the number of particles in an observation region over time. This paper studies properties of the Smoluchowski processes and considers related statistical problems. In the first part of the paper we revisit probabilistic properties of the Smoluchowski process in a unified and principled way: explicit formulas ...
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作者：Appuhamillage, Thilanka; Bokil, Vrushali; Thomann, Enrique; Waymire, Edward; Wood, Brian
作者单位：HSBC Holdings; Oregon State University; Oregon State University
摘要：The failure of a symmetry argument for the Laplace transform of a mul-tivariate density given inAnn. Appld. Probab.21(1) (2011), 183-214 wasneglected in preparation of the first errata (Ann. Appld. Probab.21(5) (2011),2050-2051). The formula for the Laplace transform is corrected in this errata
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作者：Hocquet, Antoine; Neamtu, Alexandra
作者单位：Technical University of Berlin; University of Konstanz
摘要：We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form dut - Lt(ut)ut dt = Nt(ut)dt + F(ut) d X t , where X is a gamma-H & ouml;lder rough path for gamma E ( 1 / 3 , 1/2). We explore the mild formulation that combines functional analysis techniques and controlled rough paths theory which entail the local well-posedness of such equations. We apply our results to the stochastic Landau-Lifshitz-Gilbert and Shigesada-Kawasaki-Teramoto equation.
