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Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process
We consider a discrete-time two-dimensional process
on with a supplemental process on a finite set,
where individual processes and are both skip free.
We assume that the joint process is
Markovian and that the transition probabilities of the two-dimensional process
are modulated depending on the state of the background
process . This modulation is space homogeneous except for the
boundaries of . We call this process a discrete-time
two-dimensional quasi-birth-and-death (2D-QBD) process and, under several
conditions, obtain the exact asymptotic formulae of the stationary distribution
in the coordinate directions.Comment: 54 page
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