Some Limit Theorems for Kernel-Smooth Quantile Estimators

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Functional Limit Theorems for d-dimensional FBM in HSlder Norm

In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.     

Functional Limit Theorems for the Pólya Urn

Journal of Theoretical Probability - For the plain Pólya urn with two colors, black and white, we prove a functional central limit theorem for the number of white balls, assuming that the...     

Limit theorems for extremes of strongly dependent cyclo-stationary χ-processes

In this paper, with motivation from the paper of Konstant et al. (Lith Math J 44:196-208, 2004) we derive limit theorems for the maximum of strongly dependent cyclo-stationary $\chi $ -processes. Further, under a global Hölder condition we show that Seleznjev pth-mean convergence theorem holds.     

Functional Limit Theorems for the Fractional Ornstein–Uhlenbeck Process

Journal of Theoretical Probability - We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein–Uhlenbeck process, providing the foundation for the...     

Self-Standardized Central Limit Theorems for Trimmed Lévy Processes

Journal of Theoretical Probability - We prove under general conditions that a trimmed subordinator satisfies a self-standardized central limit theorem (SSCLT). Our basic tool is a powerful...     

Ratio Limit Theorems for Random Walks and Lévy Processes

In this paper, we study quasi-symmetric random walks and Lévy processes, a property first introduced by C.J. Stone, discuss the -invariant Radon measures for random walks and Lévy processes, and formulate some nice ratio limit theorems which are closely related to -invariant Radon measures. Mathematics Subject Classifications (2000) 60G51, 60G50.Research supported in part by NSFC 10271109.     

Stable Central Limit Theorems for Super Ornstein–Uhlenbeck Processes, Ⅱ

This paper is a continuation of our recent paper(Electron. J. Probab., 24(141),(2019)) and is devoted to the asymptotic behavior of a class of supercritical super Ornstein–Uhlenbeck processes(X_t)_t≥0 with branching mechanisms of infinite second moments. In the aforementioned paper, we proved stable central limit theorems for X_t(f) for some functions f of polynomial growth in three different regimes. However, we were not able to prove central limit theorems for X     

Limit Theorems and Large Deviations for β-Jacobi Ensembles at Scaling Temperatures

Let λ=(λ₁,...,λ_n) be β-Jacobi ensembles with parameters p₁,p₂,n and β while β varying with n. Set γ=lim_n→∞ n/(p1) and σ=lim_n→∞ (p1)/(p2).In this paper,supposing lim_n→∞ log n/βn=0,we prove that the empirical measures of different scaled λ converge weakly to a Wachter distribution,a Marchenko-Pastur law and a semicircle law corresponding to σγ> 0,σ=0 or γ=0,respectively.We also offer a full large deviation principle wi...     

Central Limit Theorems for a Super-Diffusion over a Stochastic Flow

Central limit theorems of the occupation time of a superprocess over a stochastic flow are proved. For the critical and higher dimensions d≥4, the limits are Gaussian variables. For d=3, the limit is conditional Gaussian. When the stochastic flow disappears, the results degenerate to those for the ordinary super-Brownian motion.     

Limit Theorems for Critical Galton–Watson Processes with Immigration Stopped at Zero

In this paper, we consider a critical Galton–Watson branching process with immigration stopped at zero W. Some precise estimation on the probability generating function of the n-th population are obtained, and the tail probability of the life period of W is studied. Based on above results,two conditional limit theorems for W are established.     

The Pólya Sum Process: Limit Theorems for Conditioned Random Fields

Zessin (J. Contemp. Math. Anal. 44(1):36–44, 2009) constructed the so-called Pólya sum process via partial integration technique. This process shares some important properties with the Poisson process such as complete randomness and infinite divisibility. This work discusses H-sufficient statistics for the Pólya sum process as was done for the Poisson process by Nguyen and Zessin (Z. Wahrscheinlichkeitstheor. Verw. Geb. 37(3):191–200, 1976/77).     

Functional Limit Theorems for C-R Increments of l^p-Valued Wiener Processes in the Holder Norm

In this paper, based on accurately large deviation formulae established in strong topology generated by the Holder norm for l^2-valued Wiener processes, we obtain the functional limit theorems for C-R increments of l^p-valued Wiener processes in the Holder norm.     

Functional Limit Theorems for C-R Increments of k-Dimensional Brownian Motion in Hölder Norm

In this paper, based on large deviation formulas established in stronger topology generated by H?lder norm, we obtained the functional limit theorems for C-R increments of k-dimensional Brownian motion in H?lder norm Received December 19, 1999, Revised March 3, 2000, Accepted April 7, 2000     

Szegö Limit Theorems on the Sierpiński Gasket

We use the existence of localized eigenfunctions of the Laplacian on the Sierpiński gasket (SG) to formulate and prove analogues of the strong Szegö limit theorem in this fractal setting. Furthermore, we recast some of our results in terms of equally distributed sequences.     

Integro-Local Limit Theorems for Compound Renewal Processes under Cramér’S Condition. I

We obtain integro-local limit theorems in the phase space for compound renewal processes under Cramér’s moment condition. These theorems apply in a domain analogous to Cramér’s zone of deviations for random walks. It includes the zone of normal and moderately large deviations. Under the same conditions we establish some integro-local theorems for finite-dimensional distributions of compound renewal processes.     

Integro-Local Limit Theorems for Compound Renewal Processes Under Cramér’s Condition. II

We prove the statements that are formulated in the first part of this paper. As an auxiliary proposition, we establish an integro-local theorem for the renewal measure of a two-dimensional random walk.