On the Spitzer and Chung laws of the iterated logarithm for brownian motion
On the strong Brillinger-mixing property of -determinantal point processes and some applications
First, we derive a representation formula for all cumulant density functions in terms of the non-negative definite kernel function defining an -determinantal point process (DPP). Assuming absolute integrability of the function , we show that a stationary -DPP with kernel function is “strongly” Brillinger-mixing, implying, among others, that its tail--field is trivial. Second, we use this mixing property to prove rates of normal convergence for shot-noise processes and sketch some applications...
On the strong convergence for weighted sums of asymptotically almost negatively associated random variables
Applying the moment inequality of asymptotically almost negatively associated (AANA, in short) random variables which was obtained by Yuan and An (2009), some strong convergence results for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of Zhou et al. (2011), Sung (2011, 2012) to the case of AANA random variables, respectively.
On the strong law for arrays and for the bootstrap mean and variance.
On the strong law of large numbers for -dimensional arrays of random variables.
On the strong law of large numbers on some ordered structures
On the strong laws for weighted sums of -mixing random variables.
On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue
On the traces of Laguerre processes.
On the universal constant in the Katz-Petrov and Osipov inequalities
Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.
On the Weak Convergence of Stochastic Processes.
On the weak law of large numbers for normed weighted sums of i.i.d. random variables.
On the weighted Euclidean matching problem in
A partitioning algorithm for the Euclidean matching problem in is introduced and analyzed in a probabilistic model. The algorithm uses elements from the fixed dissection algorithm of Karp and Steele (1985) and the Zig-Zag algorithm of Halton and Terada (1982) for the traveling salesman problem. The algorithm runs in expected time and approximates the optimal matching in the probabilistic sense.
On the zeroes of some random functions
On the zero-one law and the law of large numbers for random walk in mixing random environment.
On The Zeros Of Oscillatory Solutions Of Linear Second-Order Differential Equations
On Valiron and Circle Convergence.
On variance conditions for Markov chain CLTs.
On weak convergence of filtrations
On Weak Convergence of Parameter Estimators of General Statistical Parametric Models