Strong approximations of bivariate uniform empirical processes
Strong consistencies of the bootstrap moments.
Strong Convergence for weighed sums of negatively superadditive dependent random variables
In this paper, the strong law of large numbers for weighted sums of negatively superadditive dependent (NSD, in short) random variables is obtained, which generalizes and improves the corresponding one of Bai and Cheng ([2]) for independent and identically distributed random variables to the case of NSD random variables.
Strong convergence for weighted sums of WOD random variables and its application in the EV regression model
The strong convergence for weighted sums of widely orthant dependent (WOD) random variables is investigated. As an application, we further investigate the strong consistency of the least squares estimator in EV regression model for WOD random variables. A simulation study is carried out to confirm the theoretical results.
Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series
The martingale Hardy space and the classical Hardy space are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from to (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a...
Strong disorder in semidirected random polymers
We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.
Strong existence, uniqueness and non-uniqueness in an equation involving local time
Strong Feller solutions to SPDE's are strong Feller in the weak topology
For a wide class of Markov processes on a Hilbert space H, defined by semilinear stochastic partial differential equations, we show that their transition semigroups map bounded Borel functions to functions weakly continuous on bounded sets, provided they map bounded Borel functions into functions continuous in the norm topology. In particular, an Ornstein-Uhlenbeck process in H is strong Feller in the norm topology if and only if it is strong Feller in the bounded weak topology. As a consequence,...
Strong hydrodynamic limit for attractive particle systems on .
Strong innovation and its applications to information diffusion modelling in finance.
Strong law of large numbers for additive extremum estimators
Extremum estimators are obtained by maximizing or minimizing a function of the sample and of the parameters relatively to the parameters. When the function to maximize or minimize is the sum of subfunctions each depending on one observation, the extremum estimators are additive. Maximum likelihood estimators are extremum additive whenever the observations are independent. Another instance of additive extremum estimators are the least squares estimators for multiple regressions when the usual assumptions...
Strong law of large numbers for branching diffusions
Let X be the branching particle diffusion corresponding to the operator Lu+β(u2−u) on D⊆ℝd (where β≥0 and β≢0). Let λc denote the generalized principal eigenvalue for the operator L+β on D and assume that it is finite. When λc>0 and L+β−λc satisfies certain spectral theoretical conditions, we prove that the random measure exp{−λct}Xt converges almost surely in the vague topology as t tends to infinity. This result is motivated by a cluster of articles due to Asmussen and Hering dating from...
Strong law of large numbers for fragmentation processes
In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than η for 1≥η>0.
Strong law of large numbers for optimal points.
Strong law of large numbers for the interface in ballistic deposition
Strong law of large numbers for -mixing sequences with different distributions.
Strong law of large numbers under a general moment condition.
Strong laws and summability for sequences of -mixing random variables in Banach spaces.
Strong laws of large numbers for arrays of rowwise conditionally independent random elements.
Strong laws of large numbers for arrays of row-wise exchangeable random elements.