Transient solutions for multidimensional denumerable state Markov processes

The computational problem of transient solutions for denumerable state Markov Processes (MPs) has been solved by Hsu and Yuan, who derived an efficient algorithm with uniform error. However, when the state 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 studied. In this paper, we study transient solutions for multidimensional denumerable state MPs and give an algorithm with uniform error. Some numerical results are presented.