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On the almost sure central limit theorem for associated random variables
the almost sure central limit theorem associated random variables
2009/9/22
The aim of this note is to prove the strong version of
the CLT for associated sequences without any strong approximation
theorems. In the proofs we only apply the weighted convergence result
for av...
Deformations of the semicircle law derived from random walks on free groups
Deformations of the semicircle law random walks on free groups
2009/9/22
New l-parameter families of central limit distributions
are investigated by means of random walks on trees associated with
free groups under two kinds of states: one is Haagerup's function and
the ...
A non-ergodic phenomenon for some random dynamical system
A non-ergodic phenomenon some random dynamical system
2009/9/22
In [2] Jajte formulated the following question:
Let h,(x) and hi (x) be homeomorphisms of the interval LO, 11
onto itself. Is it true that for any ~ � 1 01,1 and almost any t ~ ( 01,)
there exists ...
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...
The ladder variables of a Markov random walk
Markov random walks ladder variables Harris recurrence regeneration epochs coupling
2009/9/22
Given a Harris chain (M,,)n40 on any state space
(9C,) with essentially unique stationary measure <, let (Xn)nZObe
a sequence of real-valued random variables which are conditionally
independent, gi...
Vertices of degree one in a random sphere of influence graph
Vertices of degree one a random sphere of influence graph
2009/9/22
The sphere of influence graph of the set of vertices in R~
is constructed by identifying the nearest neighbour of each vertex,
centering a ball at each vertex so that its nearest neighbour lies on t...
On some connections between random partitions of the unit segment and the Poisson process
some connections random partitions of the unit segment the Poisson process
2009/9/22
Let D, be the diameter of a partition of the interval [0, t]
by renewal moments of a standard Poisson process. Then DJln t + 1 for
t + co, in probability. Other theorems on diameters are obtained. J...
On the Multimodality of Random Probability Measures
convexity Dirichlet process multimodal distribution functions random probability measures
2009/9/22
Nonparametric methods for density estimation are examined here.
Within a Bayesian setting the construction of an absolutely continuous random
probability measure is often required for nonparametric ...
Integral priors for the one way random effects model
Bayesian model selection Integral priors Intrinsic priors Random effects model Recurrent Markov chains
2009/9/22
The one way random effects model is analyzed from the Bayesian
model selection perspective. From this point of view Bayes factors are the key
tool to choose between two models. In order to produce ...
Spectral representation and extrapolation of stationary random processes on linear spaces
Spectral representation extrapolation of stationary random processes linear spaces
2009/9/21
The paper deals with continuous Banach-space-valued
stationary random processes on linear spaces. From von Waldenfels'
1131 integral representation of positive definite functions on a linear
space ...
Recurrence theorems for Markov random walks
Markov random walk random walk with stationary increments recurrence point
2009/9/21
Let (M,, SJnao be a Markov random walk whose
driving chain (M,JnbwDith general. state space (9,G ) is ergodic with
unique stationary distribution 4. Providing n- S, + 0 in probability
under PI,it i...
Max-semistable hemigroups: structure, domains of attraction and limit theorems with random sample size
Extreme values max-semistable distributions hemigroup max-semiselfdecomposability
2009/9/21
Let (X,) be a squence of independent real vatued random
variabl~sA. suitable convergk:nce condition far affine normalimned
maxima of (XJ k @given in the seBLjstable setup, i.e. fur inmasing
samplir...
On the approximation of a random variable by a conditioning of a given sequence
Condtional expectation almost sure convergence stochastics onvergence
2009/9/21
Let (a,$ Pj,I IN a non-atomic probability spa- If(Xw)
is a sequenm 5f r.y.'s satisry'ying X, -+ Q as. (respeclitrely, in probability)
a s n - , ~ and EX:-+ca, EX;-=+w as n-roo, th@n for any tv. Y
t...
Asymptotic behavior of some random splitting schemes
Splitting schemes asymptotic behavior Markov chains stationary distribution contraction principle
2009/9/21
We consider three new schemes of random splitting of
a unit interval. These schemes am related to settings considered earlier
in literature. Essentially we are concerned with asymptotic behavior of
...
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...