The Number of Visits Until Absorption to Subsets of the State Space by a Discrete-Parameter Markov Chain: the Multivariate Case

Abstract

In Corollary 2.6, we have considered the variable ${M_{{A_1}}}$ the number of visits to A₁ until absorption by a chain Z = { Z₀, Z₁, … } whose state space is partitioned as A₁ ∪ A₂ ∪ {ω} with ω being the absorbing state. There, the probability mass function of${M_{{A_1}}}$ was deduced from our main results on sojourn times. On the other hand, the power of the generalised renewal argument was demonstrated in Section 2.1.3. In this chapter, these two threads will be combined to obtain results on the joint distribution of the number of visits to a subset of the state space whose set of transient states is partitioned into possibly more than two subsets.