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作者：Baker, Graeme; Shkolnikov, Mykhaylo
作者单位：Columbia University; Carnegie Mellon University
摘要：We consider a probabilistic formulation of a singular two-phase Stefan problem in one space dimension, which amounts to a coupled system of two McKean-Vlasov stochastic differential equations. In the financial context of systemic risk, this system models two competing regions with a large number of interconnected banks or firms at risk of default. Our main result shows the existence of a solution whose discontinuities obey the natural physicality condition for the problem at hand. Thus, this w...
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作者：Imkeller, Peter; Pellat, Rhoss likibi; Menoukeu-pamen, Olivier
作者单位：Humboldt University of Berlin; University of Liverpool
摘要：In this paper, we consider quadratic forward-backward SDEs (QFBSDEs), for which the drift in the forward equation does not satisfy the standard globally Lipschitz condition and the driver of the backward system possesses nonlinearity of type f (|y|)|z|2, where f is any locally integrable function. We prove both the Malliavin and classical differentiability of solutions to this type of QFBSDEs and provide representations of these derivatives processes. As a by-product, we derive a representatio...
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作者：Wang, Tianhao; Zhong, Xinyi; Fan, Zhou
作者单位：Yale University
摘要：Approximate message passing (AMP) algorithms provide a valuable tool for studying mean-field approximations and dynamics in a variety of applications. Although these algorithms are often first derived for matrices having independent Gaussian entries or satisfying rotational invariance in law, their state evolution characterizations are expected to hold over larger universality classes of random matrix ensembles. We develop several new results on AMP universality. For AMP algorithms tailored to...
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作者：Emilia Caballero, Maria; Gonzalez Casanov, Adrian; Perez, Jose-Luis
作者单位：Universidad Nacional Autonoma de Mexico
摘要：When two (possibly different in distribution) continuous-state branching processes with immigration are present, we study the relative frequency of one of them when the total mass is forced to be constant at a dense set of times. This leads to a SDE whose unique strong solution will be the definition of a Lambda-asymmetric frequency process (Lambda-AFP). We prove that it is a Feller process and we calculate a large population limit when the total mass tends to infinity. This allows us to study...
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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...
