On the Equivalence of Two Expected Average Cost Criteria for Semi-Markov Control Processes

References

• Bertsekas D. P., Shreve S. E.Stochastic Optimal Control: The Discrete Time Case (1978) (Academic Press, New York) Google Scholar
• Blackwell D. A renewal theorem. Duke Math. J. (1948) 15:145–150Crossref, Google Scholar
• Brown L. D., Purves R. Measurable selections of extrema. Ann. Statist. (1973) 1:902–912Crossref, Google Scholar
• Feinberg E. A. Constrained semi-Markov decision processes with average rewards. Math. Methods Oper. Res. (1994) 39:257–288Crossref, Google Scholar
• Hernández-Lerma O., Lasserre J. B.Further Topics on Discrete-Time Markov Control Process (1999) (Springer-Verlag, New York) Crossref, Google Scholar
• Hernández-Lerma O., Luque-Vásquez F. Semi-Markov control models with average costs. Applicationes Mathematicae (1999) 26:315–331Crossref, Google Scholar
• Jaśkiewicz A. An approximation approach to ergodic semi-Markov control processes. Math. Methods Oper. Res. (2001) 54:1–19Crossref, Google Scholar
• Jaśkiewicz A. Zero-sum semi-Markov games. SIAM J. Control Optim. (2002) 41:723–739Crossref, Google Scholar
• Maitra A. P., Sudderth W. D.Discrete Gambling and Stochastic Games (1996) (Springer-Verlag, New York) Crossref, Google Scholar
• Meyn S. P., Tweedie R. L.Markov Chains and Stochastic Stability (1993) (Springer-Verlag, New York) Crossref, Google Scholar
• Meyn S. P., Tweedie R. L. Computable bounds for geometric convergence rates of Markov chains. Ann. Appl. Probab. (1994) 4:981–1011Crossref, Google Scholar
• Mine H., Osaki S.Markovian Decision Processes (1970) (Elsevier, New York) Google Scholar
• Neveu J.Mathematical Foundations of the Calculus of Probability (1965) (Holden-Day, San Francisco, CA) Google Scholar
• Neveu J.Discrete-Parameter Martingales (1975) (Elsevier, New York) Google Scholar
• Nowak A. S. Universally measurable strategies in zero-sum stochastic games. Ann. Probab. (1985) 13:269–287Crossref, Google Scholar
• Nowak A. S. Some remarks on equilibria in semi-Markov games. Applicationes Mathematicae (2000) 27:385–394Crossref, Google Scholar
• Nowak A. S., Altman E. ε-Equilibria for stochastic games with uncountable state space and unbounded costs. SIAM J. Control Optim. (2002) 40:1821–1839Crossref, Google Scholar
• Puterman L. M.Markov Decision Processes (1994) (John Wiley, New York) Crossref, Google Scholar
• Ross S. M.Applied Probability Models with Optimization Applications (1970) (Holden-Day, San Francisco, CA) Google Scholar
• Schäl M. On the second optimality equation for semi-Markov decision models. Math. Oper. Res. (1992) 17:470–486Link, Google Scholar
• Sennott L. I. Average cost semi-Markov decision processes and the control of queueing system. Probab. Engrg. and Inform. Sci. (1989) 3:247–272Crossref, Google Scholar
• Strauch R. E. Negative dynamic programming. Ann. Statist. (1966) 37:871–890Crossref, Google Scholar
• Yushkevich A. On semi-Markov controlled models with an average reward criterion. Theory Probab. Appl. (1981) 26:796–803Crossref, Google Scholar
• Vega-Amaya O., Luque-Vásquez F. Sample-path average cost optimality for semi-Markov control processes on Borel spaces: Unbounded costs and mean holding times. Applicationes Mathematicae (2000) 27:343–367Crossref, Google Scholar