We consider a random measure defined by the occu-pation time of Brownian motion in ι. If it is normalized λlog λthen we show that its cluster set as λlongrightarrow can be represented by Ι-function on -finite measure in ι

In the present paper we provide a short of the uni-form CLT for the function-indexed martingale difference process under the uniformly integrable entropy by establishing a maximal inequality.

In this article we prove a central limit theorem for strictly stationary weakly dependent random fields with some interlaced mix-ing conditions. Mixing coefficients are not assumed. The result it basically the same to Peligrad([4]), which is CLT weakly depen-dent arrays of random variables. The proof is quite similar to the of Peligrad.

We consider ΜΑΡ/G/ 1 finite capacity queue with mul-tiple thresholds on buffer. The arrival of customers follows a Markov-ian arrival process(MAP). The service time of a customer depends on the queue length at service initiation of the customer. By using the embeded Markov chain method and the supplementary variable method, we obtain the queue length distribution ar departure epochs and at arbitrary epochs. This gives the loss probability and the mean waiting time by Little's law. We also give a simple numerical examples to apply the overload control in packetized networks.

Let the given distribution have a log-concave density which is proportional to exp(-V(x)) on R\ulcorner. We consider a Markov chain induced by the method Gibbs sampling having as its in-variant distribution and prove geometric ergodicity and the functional central limit theorem for the process

We provide a generalization of Whipple's Whipple's quadratic transformation formula for F.

The object of this note is to give sums of certain families of series which are initiated from their special cases considered here. Pelevant connections of the series identities presented here with those given elsewhere are also pointed out.