-
作者：Crawford, Nicholas; Rosenthal, Ron
作者单位：Technion Israel Institute of Technology
摘要：The complex Ginibre ensemble is the distribution of an N x N nonHermitian random matrix over C with i.i.d. complex Gaussian entries normalized to have mean zero and variance 1/N. Unlike the Gaussian unitary ensemble, for which the eigenvectors are distributed according to Haar measure on the compact group U (N), independently of the eigenvalues, the geometry of the eigenbases of the Ginibre ensemble are not particularly well understood. In this paper we systematically study properties of eigen...
-
作者：Cardaliaguet, Pierre; Souganidis, Panagiotis E.
作者单位：Universite PSL; Universite Paris-Dauphine; University of Chicago
摘要：We consider mean field games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution exists and is unique for monotone coupling functions. We also use the solution to find approximate optimal strategies (Nash equilibria) for N-player differential games with common but no idiosyncratic noise. An important step in the analysis is the study of the...
-
作者：Backhoff, Julio; Bartl, Daniel; Beiglbock, Mathias; Wiesel, Johannes
作者单位：University of Twente; University of Vienna; Columbia University
摘要：A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and connections to various areas (e.g., Plug-Pichler-stochastic programming, Hellwig-game theory, Aldous-stability of optimal stopping, Hoover-Keisler-model theory). Remarkably, all these seemingly independent approaches define the same adapted weak topology in finite...
-
作者：Horst, Ulrich; Xia, Xiaonyu; Zhou, Chao
作者单位：Humboldt University of Berlin; Humboldt University of Berlin; Wenzhou University; City University of Hong Kong
摘要：We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semilinear PDE with superlinear gradient, monotone generator and singular terminal value. We also establish an asymptotic analysis of the robust model for small amounts of uncertainty and analyze the effect of robustness on optimal trading strategies and liquidation costs. In...
-
作者：Owada, Takashi
作者单位：Purdue University System; Purdue University
摘要：The objective of this paper is to examine the asymptotic behavior of persistence diagrams associated with Cech filtration. A persistence diagram is a graphical descriptor of a topological and algebraic structure of geometric objects. We consider Cech filtration over a scaled random sample r(n)(-1) chi(n) = {r(n)(-1) x(1), ..., r(n)(-1) X-n}, such that r(n) -> 0 as n -> infinity. We treat per- sistence diagrams as a point process and establish their limit theorems in the sparse regime: nr(n)(d)...
-
作者：Addario-Berry, Louigi; Lin, Jessica; Tendron, Thomas
作者单位：McGill University; University of Oxford
摘要：We establish an invariance principle for the barycenter of a Brunet-Derrida particle system in d dimensions. The model consists of N particles undergoing dyadic branching Brownian motion with rate 1. At a branching event, the number of particles is kept equal to N by removing the particle located furthest away from the barycenter. To prove the invariance principle, a key step is to establish Harris recurrence for the process viewed from its barycenter.
-
作者：Pang, Guodong; Pardoux, Etienne
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We study non-Markovian stochastic epidemic models (SIS, SIR, SIRS, and SEIR), in which the infectious (and latent/exposing, immune) periods have a general distribution. We provide a representation of the evolution dynamics using the time epochs of infection (and latency/exposure, immunity). Taking the limit as the size of the population tends to infinity, we prove both a functional law of large number (FLLN) and a functional central limit theorem (FCLT) for the processes of interest in these m...
-
作者：Alberts, Tom; Normand, Raoul
作者单位：Utah System of Higher Education; University of Utah; New York University
摘要：We study the dimension properties of the spectral measure of the circular beta-ensembles. For beta >= 2 it was previously shown by Simon that the spec-tral measure is almost surely singular continuous with respect to Lebesgue measure on partial differential D and the dimension of its support is 1 - 2/beta. We reprove this result with a combination of probabilistic techniques and the so-called Jitomirskaya-Last inequalities. Our method is simpler in nature and mostly self-contained, with an emp...
-
作者：Kumar, Chaman; Neelima; Reisinger, Christoph; Stockinger, Wolfgang
作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Roorkee; University of Delhi; University of Oxford
摘要：In this paper, we first establish well-posedness of McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs) with common noise, possibly with coefficients of super-linear growth in the state variable. Second, we present stable time-stepping schemes for this class of McKean-Vlasov SDEs. Specifically, we propose an explicit tamed Euler and tamed Milstein scheme for an interacting particle system associated with the McKean-Vlasov equation. We prove stability and strong convergence of ...
-
作者：Yao, Jianfeng; Yuan, Wangjun
作者单位：The Chinese University of Hong Kong, Shenzhen; University of Hong Kong
摘要：In this article, we establish a limiting distribution for eigenvalues of a class of autocovariance matrices. The same distribution has been found in the literature for a regularized version of these autocovariance matrices. The original nonregularized autocovariance matrices are noninvertible, thus introducing supplementary difficulties for the study of their eigenvalues through Girko's Hermitization scheme. The key result in this paper is a new polynomial lower bound for a specific family of ...
