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Decomposition of convolution semigroups on groups and the 0-1 law
Decomposition of convolution semigroups groups and the 0-1 law
2009/9/22
Let (X (t))a,o be a stochastically continuous symmetric
Levy process with values in a complete separable group G. We denote
by h),,,, the semigroup of one-dimensional distributions of X(t). Suppose
...
Convergence rates in the strong law for associated random variables
Convergence rates in the strong law associated random variables
2009/9/22
We prove the Marcinkiewicz-Zygmund SLLN (MZ-
-SLLN) of order p, ~ � 1 12,[ , br associated sequences, not necessarily
stationary. Our assumption on the moment of the random variables is
minimal. We...
On Paul Lévy's arc sine law and Shiga-Watanabe's time inversion result
Paul Lévy's arc sine law Shiga-Watanabe's time inversion result
2009/9/22
Let ((XJ,P) be a symmetric real-valued H-self-similar
diffusion starting at 0. We characterize the distributions of A,, the time
spent on (0, a) before time t, and a,, the time of the last visit to
...
A generalized Law of the Iterated Logarithm for the largest observation of a triangular array
Almost sure convergence weak law of large numbers law of the iterated logarithm
2009/9/21
Consider independent and identically distributed random
variables (X, XRj, I < j < k, k > 1) from a particular distribution
with EX = oo. We show that there exists an unusual generalized
Law of the...
Marcinkiewicz-type strong law of large numbers for pairwise independent random fields
Marcinhewin strong law d large numbers pairwise independent random variables random fields
2009/9/21
We present the Marcinkiewicz-type strong law of large
numbers for random fields {X,, n E Zd,) of pairwise independent random
variables, where Zd,, d & 1, is the set of positive d-dimensional
lattic...
On Hartman's law of iterated logarithm for explosive Gaussian autoregressive processes
Autoregressive Gaussian process law of iterated logarithm maximum likelihood estimation
2009/9/21
A law of iterated logarithm is established lot the maximum
likelihood estimator of the unknown parameter of the explosive
Gaussian autoregressive process. Outside the Gaussian case, we show
that th...
Law of iterated logarithm for subsequences of partial sums which are in domain of partial attraction of a semistable law
Law of iterated logarithm subsequences domain of partial attraction semistable law
2009/9/21
Let (X,, n 2 1) be a sequence of independent identically
distributed random variables with a common distribution function
F and let S,, = xy=,Xj, n 2 1. When F belongs to the domain of
partial attr...
CONVERGENCE RATES IN THE LAW OF LARGE NUMBERS FOR ARRAYS
Arrays of rowwise independent random variables complete convergence
2009/9/18
In this paper we present new suficient conditions for
complete convergence for $urns of arrays of rowwise independent random
variables. These conditions appear to be necessary and sufficient
in the...
ON THE STRONG LAW OF LARGE FOR SEQUENCES OF BLOCKWISE INDEPENDENT AND BLOCKWISE p-ORTNOGONA RANDOM ELEMENTS IN RADEMACWER TYPE p BANACW SPACES
Blockwise independent random elements blockwise p-orthogonal random elements almost sure convergence
2009/9/18
For a sequence of random elements {G, n 2 1) taking
values in a real separable Rademacher type p (1 < p < 2) Banach space
and positive constants b,l 7 co, conditions are provided for the strong
law...
The Law of Categorical Judgment Revisited。
Central limit theorems in linear structural error-in-variables models with explanatory variables in the domain of attraction of the normal law
central limit theorem domain of attraction of the normal law large-sample approximate confidence interval self-normalization Studentization
2009/9/16
Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (C...
A limited in bandwidth uniformity for the functional limit law of the increments of the empirical process
Empricial processes Functional limit theorems Strong theorems Density estimation LATEX2ε
2009/9/16
Consider the following local empirical process indexed by $K in mathcal{G}$, for fixed $h>0$ and $z in mathbb{R}^d$: $$G_n(K,h,z):=sum_{i=1}^n K (frac{Z_i-z}{h^{1/d}}) - mathbb{E} (K (frac{Z_i-z}{h^{1...
The Law of Large Numbers for U-statistics Under Absolute Regularity
Law of large numbers U-statistics absolute regularity
2009/5/8
We prove the law of large numbers for U-statistics whose underlying sequence of random variables satisfies an absolute regularity condition ($beta$-mixing condition) under suboptimal conditions.
A Weak Law of Large Numbers for the Sample Covariance Matrix
Law of large numbers,affine normalization sample covariance domain of attraction generalized domain of attraction
2009/5/4
In this article we consider the sample covariance matrix formed from a sequence of independent and identically distributed random vectors from the generalized domain of attraction of the multivariate ...
A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment
random walk in random environment RWRE law of large numbers
2009/4/29
We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general...