ON THE CONVERGENCE OF GLOBAL RATIONAL APPROXIMANTS FOR STOCHASTIC DISCRETE-EVENT SYSTEMS

Difficulties often arise in analyzing stochastic discrete event system s due to the so-called ''curse of dimensionality''. A typical example is the computation of some integer-parameterized functions, where the integer parameter represents the system size or dimension. Rational ap proximation approach has been introduced to tackle this type of comput ational complexity. The underline idea is to develop rational approxim ants with increasing orders which converge to the values of the system s. Various examples demonstrated the effectiveness of the approach. In this paper we investigate the convergence and convergence rates of th e rational approximants. First, a convergence rate of order O (1/root n) is obtained for the so-called Type-1 rational approximant sequence. Secondly, we establish conditions under which the sequence of [n/n] T ype-2 rational approximants has a convergence rate of order O (n(alpha )e(-beta root n)).