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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...
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 ...
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 ...
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...
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...
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...
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...
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 ...
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 ...
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 ...
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...
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...
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...
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 ...
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...

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