Let {Xn, n = 0} be a Markov chains with the state space S = {1, 2, ..., m}, and the probability distribution P(x0) [Pi]nk=1Pk(xkxk-1), where Pk(ji) is the transition probability P(Xk = jXk-1 = i). Let gk(i, j) be the functions defined on S x S, and let Fn([omega]) = (1/n)[Sigma]nk=1gk(Xk-1, Xk)....

Let {Xn,n [greater-or-equal, slanted] 0} be nonhomogeneous Markov chain with state space S = {1,2, ..., m} and transition probabilities pn(i,j). In this paper some strong limit theorems relative to the geometric average of the random transition probabilities {pk(Xk-1,Xk), 1[less-than-or-equals,...

Let Xn, n [greater-or-equal, slanted] 0 be a sequence of successive letters produced by a nonhomogeneous Markov information source with alphabet S = 1,2, ...,m, and the probability distribution p(x0)[Pi]kn = 1 pk(xk-1, xk), where pk(i,j) is the transition probability P(Xk = jXk-1 = i). Let...

Using the notion of likelihood ratio, the limit properties of the sequences of dependent nonnegative integer-valued ndom variables are studied, and a kind of strong limit theorem represented by inequalities, or the strong deviation eorem, is obtained. In the proof an approach of applying the...

In this paper, the notion of likelihood ratio, as a measure of the deviation between a sequence of integer-valued random variables and an independent random sequence with Poisson distribution is introduced, and a class of strong laws, expressed by inequalities, on certain sets determined by this...

In this paper, by means of the notion of likelihood ratio and by using an analytical technique for the investigation of a.e. convergence presented, an extension of a theorem on the gambling system to arbitrary binary random sequences is obtained.

The conventional data envelopment analysis (DEA) assumes that the inputs and outputs are real values. However, in many real world instances, some inputs and outputs must be in integer values. While integer-valued DEA models have been proposed, the current paper develops an integer-valued DEA...