Poisson approximation for some point processes in reliability

In this paper, we consider a failure point process related to the Markovian arrival process defined by Neuts. We show that it converges in distribution to a homogeneous Poisson process. This convergence takes place in the context of rare occurrences of failures. We also provide a convergence rate of the convergence in total variation of this point process using an approach developed by Kabanov, Liptser and Shiryaev for the doubly stochastic Poisson process driven by a finite Markov process.

Poisson approximation for some point processes in reliability

In this paper, we consider a failure point process related to the Markovian arrival process defined by Neuts. We show that it converges in distribution to a homogeneous Poisson process. This convergence takes place in the context of rare occurrences of failures. We also provide a convergence rate of the convergence in total variation of this point process using an approach developed by Kabanov, Liptser and Shiryaev for the doubly stochastic Poisson process driven by a finite Markov process.

Comparison of Redundancy of French and English through Use of a Regular Finite Markov Process

Digram transitional probabilities were used to compare the uncertainty of the English and French languages. An equilibrium matrix ( A), an average information ( H) value and the redundancy ( C) were computed for both languages using a regular Markov process. Six exponentiations were required to reach an equilibrium with a maximum absolute deviation of 0.005. The value of H for English and French was 4.11 bits and 3.96 bits respectively. Redundancy C for English was 12.6% and for French 15.8%. Differences between languages were observed warranting caution in the use of sequential dependencies of letters in inter-language studies.

An indication of the asymptotic nature of the mendelian Markov process

Consider a finite Markov process {Xn } described by the one-step transition probabilities In describing the transition probabilities in the above manner we are adopting the convention that (0)0 = 1 so that the states 0 and M are absorbing, and the states 1,2,···,M-1 are transient.

An indication of the asymptotic nature of the mendelian Markov process

Consider a finite Markov process {Xn} described by the one-step transition probabilities In describing the transition probabilities in the above manner we are adopting the convention that (0)0 = 1 so that the states 0 and M are absorbing, and the states 1,2,···,M-1 are transient.