Approximating the Approximation

• Published in: Labelled Markov Processes pp. 147 - 152
• Main Author: Prakash Panangaden
• Format: Book Chapter
• Language: English
• Published: Singapore World Scientific Publishing Company 2009; IMPERIAL COLLEGE PRESS
• Subjects: Mathematical theory of computation
• ISBN: 9781848162877; 1848162871; 190897866X; 1848162898; 9781908978660; 9781848162891
• DOI: 10.1142/9781848162891_0010

The approximation schemes described in the last chapter have nice mathematical properties, but can we really use them in practice? A number of problems arise when one attempts the approximation construction. The most vexing is that the number of states rises very rapidly. The second problem is that many of the states, which are subsets of the original continuous state space, become very small. The third problem is that these subsets may be very “nasty”; they are only required to be measurable. In this section we describe work reported in [BCFPP05] where Monte Carlo techniques were used to alleviate some of these problems. There are still, however, many obstacles to using these techniques in practice and it is the subject of active investigation…