Recursive Moment Formulas for Semi-Markov Processes.
STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH
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Let X Xtt or 0 be an irreducible semi-markov process SMP on countable state space E. For fixed Z an element of E, let Tz inft or 0Xt-not z, Xtz and set Yf integral from 0 to T sub z of fXtdt, where f E approaches R is an arbitrary function. Our objective is to study the mixed moments of the form E pi from i 1 to r of Yf sub i, when f sub i E approaches R is an arbitrary function, for i 1,2,...r, and r is a positive integer. This quantity is especially relevant to the regenerative simulation. Also, several useful variations and generalizations are introduced and studied. Keywords Semi-Markov processes regenerative simulation recursive moments.
- Statistics and Probability