Summary
We consider the stopping time problems whose costs are given by time average forms, a generalization of the Gittins index. We show the existence of the optimal solutions and give their approximation to these stopping time problems.
References
Bensoussan, A., Lions, J.L.: Applications des inéquations variationelles en contrôle stochastique. Paris: Dunod 1978
Bensoussan, A., Lions, J.L.: Contrôle impulsionnel et inéquations quasi-variationnelles. Paris: Dunod 1982
Bismut, J.M., Skalli, B.: Temps d'arrêt optimal, théorie générale de processus et processus de Markov. Z. Wahrscheinlichkeistheor. Verw. Geb.39, 301–313 (1977)
Hanouzet, B., Joly, J.L.: Convergence uniforme des itérés définissant la solution d'une inéquation quasi variationnelle. C. R. Acad. Sci., Paris286, 735–738 (1978)
Karatzas, I.: Gittins indices in the dynamic allocation problem for diffusion processes. Ann. Probab.12, 173–192 (1984)
Morimoto, H.: Dynkin games and martingale methods. Stochastics13, 213–228 (1984)
Morimoto, H.: Optimal switching for alternating processes. Appl. Math. Optimization16, 1–17 (1987)
Robin, M.: On some impulse control problems with long run anverage cost. SIAM J. Control Optimization19, 333–358 (1981)
Robin, M.: Long-term average cost control problems for continuous time Markov processes: A survey. Acta Appl. Math.1, 281–299 (1983)
Stettner, L.: On ergodic impulsive control problems. Stochastics18, 49–72 (1986)
Sun, M.: An optimal stopping time problem with time average cost in a bounded interval. Syst. Control Lett.8, 173–180 (1986)
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Morimoto, H. On average cost stopping time problems. Probab. Th. Rel. Fields 90, 469–490 (1991). https://doi.org/10.1007/BF01192139
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DOI: https://doi.org/10.1007/BF01192139
Keywords
- Stochastic Process
- Probability Theory
- Average Form
- Mathematical Biology
- Average Cost