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作者：Yin, Yanqing; Ma, Yanyuan
作者单位：Chongqing University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is to study the properties of eigenvalues and eigenvectors of high-dimensional sample correlation matrices. We first improve the result of Jiang (Sankhya over bar 66 (2004) 35-48), Xiao and Zhou (J. Theoret. Probab. 23 (2010) 1-20) and the Theorem 1 of El Karoui (Ann. Appl. Probab. 19 (2009) 2362-2405), both concerning the limiting spectral distribution and the ex-treme eigenvalues of sample correlation matrices, by allowing a more general fourth moment condition. Then, we establish...
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作者：Kallblad, Sigrid
作者单位：Royal Institute of Technology
摘要：We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales enables us to transform the distributional constraint into an initial condition and view the problem as a stochastic control problem; we establish the corresponding dynamic programming principle. The method offers a systematic approach for solving the problem for general constraints and under weak assumptions o...
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作者：Olesker-Taylor, Sam
作者单位：University of Bath
摘要：Consider N stations interconnected with links, each of capacity K, forming a complete graph. Calls arrive to each link at rate lambda and depart at rate 1. If a call arrives to a link xy, connecting stations x and y, which is at capacity, then a third station z is chosen uniformly at random and the call is attempted to be routed via z: if both links xz and zy have spare capacity, then the call is held simultaneously on these two; otherwise the call is lost. We analyse an approximation of this ...
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作者：Jorritsma, Joost; Komjathy, Julia
作者单位：Eindhoven University of Technology; Delft University of Technology
摘要：We study the evolution of the graph distance and weighted distance between two fixed vertices in dynamically growing random graph models. More precisely, we consider preferential attachment models with power -law exponent tau e (2, 3), sample two vertices ut, vt uniformly at random when the graph has t vertices and study the evolution of the graph dis-tance between these two fixed vertices as the surrounding graph grows. This yields a discrete-time stochastic process in t' > t, called the dis-...
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作者：Fang, Rongjuan; Li, Zenghu
作者单位：Fujian Normal University; Beijing Normal University
摘要：A continuous-state branching process in varying environments is constructed by the pathwise unique positive solution to a stochastic integral equation driven by time-space noises. The cumulant semigroup of the process is characterized in terms of a backward integral equation. We clarify the behavior of the process at its bottlenecks, which are the deterministic times when it arrives at zero almost surely by negative jumps. The process arises naturally as the scaling limit of Galton-Watson proc...
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作者：Fountoulakis, Nikolaos; Iyer, Tejas; Mailler, Cecile; Sulzbach, Henning
作者单位：University of Birmingham; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Bath
摘要：We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula generalises results for a number of existing models, including random Apollonian networks and the weighted random recursive tree. It also confirms results on the scale-free nature of complex quantum network manifolds in dimensions d > 2, and special types of network geometry with Flavour models studied in the physics literature by Bianconi and R...
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作者：Doebler, Christian; Kasprzak, Mikolaj J.; Peccati, Giovanni
作者单位：Heinrich Heine University Dusseldorf; University of Luxembourg
摘要：We consider sequences of U-processes based on symmetric kernels of a fixed order, that possibly depend on the sample size. Our main contribution is the derivation of a set of analytic sufficient conditions, under which the aforementioned U-processes weakly converge to a linear combination of time-changed independent Brownian motions. In view of the underlying symmetric structure, the involved time-changes and weights remarkably depend only on the order of the U-statistic, and have consequently...
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作者：Dombry, Clement; Tillier, Charles; Wintenberger, Olivier
作者单位：Universite Marie et Louis Pasteur; Universite Paris Saclay; Universite Paris Cite; Sorbonne Universite
摘要：We consider regular variation for marked point processes with independent heavy-tailed marks and prove a single large point heuristic: the limit measure is concentrated on the cone of point measures with one single point. We then investigate successive hidden regular variation removing the cone of point measures with at most k points, k >= 1, and prove a multiple large point phenomenon: the limit measure is concentrated on the cone of point measures with k + 1 points. We show how these results...
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作者：Bo, Lijun; Liao, Huafu; Yu, Xiang
作者单位：Xidian University; National University of Singapore; Hong Kong Polytechnic University
摘要：This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated under partial observations of asset prices and sequential default events. By establishing a martingale representation theorem based on incomplete and phasing out filtration, we c...
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作者：De Angelis, Tiziano; Merkulov, Nikita; Palczewski, Jan
作者单位：University of Turin; University of Leeds
摘要：We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general cadlag measurable processes. As a by-product of our method of proof we also obtain existence of optimal strategies for both players. The main novelties are that we do not assume a Markovian nature of the game nor a particular structure of the information available to the players. This allows us to go beyon...
