The computational problem of transient solutions for denumerable state
Markov Processes (MP's) has been solved by Hsu and Yuan [12], who der
ived an efficient algorithm with uniform error. However, when the stat
e space of an MP is of two or more dimensions, even for computational
methods dealing with stationary solutions, only the case where one of
the dimensions is infinite and all the others are finite has been stud
ied. In this paper, we study transient solutions for multidimensional
denumerable state MP's and give an algorithm with uniform error. Some
numerical results are presented.