Let {qn, n [greater-or-equal, slanted] 0} be a sequence of positive integers, In = {0, 1, ..., qn}, {Xn, n [greater-or-equal, slanted] 0} a sequence of random variables, where Xn takes on values in In, and P(X1 = x1, ..., Xn = xn) 0, for all xi [epsilon] Ii, 0 [less-than-or-equals, slant] i...

A strong limit theorem on gambling system for Bernoulli sequences is extended to the sequences of arbitrary discrete random variables by using the conditional probabilities. Furthermore, by allowing the selection function to take values in an interval, the conception of random selection is...

In this paper, the strong limit theorems for arbitrary stochastic sequences are studied. Some convergence theorems for martingale difference sequence and a class of strong limit theorem for countable nonhomogeneous Markov chains are the particular cases of the results of this paper. Finally, the...

Let {Xn,n[greater-or-equal, slanted]0} be a sequence of random variables taking values in S={1,2,...,N}, and let pk(xk x0,...,xk-1)=P(Xk=xk X0=x0,...,Xk-1=xk-1). In this paper a theorem on a.e. convergence for the harmonic mean of the random conditional probabilities {pk(Xk X0,...,Xk-1),...

In this paper, we use an analytic approach to study the limit properties of {inn(Xn)}, the functional of a countable nonhomogeneous Markov chain {Xn}. A class of strong laws of large numbers for these processes, which are different from the usual ones, are obtained. In the theorems of this...

In this paper, we study the strong law of large numbers on the frequencies of states for a Markov chains field on a Bethe tree. In the proof, we apply a new technique in the study of the strong limit theorem.

Combining the disputes on the “normal development†and “natural growth existing in farmers†cooperatives and according to the actual investigation statistics, the management model selection and regulation (including model selection, policy encouragement, operation scale and...

Along with high-speed economic development and increasing energy consumption, the Chinese Government faces a growing pressure to maintain the balance between energy supply and demand. In 2009, China has become both the largest energy consumer and CO2 emitting country in the world. In this case,...

Let {Xn, n[greater-or-equal, slanted]0} be a sequence of random variables on the probability space ([Omega],F,P) taking values in the alphabet S={1,2,...,N}, and Q be another probability measure on F, under which {Xn, n[greater-or-equal, slanted]0} is a Markov chain. Let h(P Q) be the sample...

Renewable energy is one of the possible solutions when addressing climate change. Today, large-scale renewable energy integration needs to include the experience to balance the discrepancy between electricity demand and supply. The electrification of transportation may have the potential to deal...