A discrete time Markov decision process under a fractional discounted reward criterion
*Teruo TanakaCorresponding authorteruo@hiroshima-cu.ac.jpDepartment of Systems EngineeringGraduate School of Information Sciences3-4-1, OzukahigashiHiroshima City UniversityAsaminami-ku, Hiroshima, 731-3194, JapanView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Jun 2022
- Accepted:
- 09 Nov 2022
- Published Online:
- 02 Feb 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1329
- Pages:
- 1237–1247
Abstract
Keywords
Subject Classifications
References
[1] Vijay Kumar Aggarwal, Ramaswamy Chandrasekaran, and Kunhiraman P. K. Nair, “Markov ratio decision processes,” Journal of Optimization Theory and Applications, vol. 21, pp. 27–37 (1977).
[2] Dimitri P. Bertsekas and Steven E. Shreve, Stochastic Optimal Control. New York, NY, USA: Academic Press (1978).
[3] Onesimo Hernández-Lerma, Adaptive Markov Control Processes. New York, NY, USA: Springer-Verlag (1989).
[4] Onesimo Hernández-Lerma and Jean Bernard Lasserre, Discrete-Time Markov Control Processes. New York, NY, USA: Springer-Verlag (1996).
[5] Seiichi Iwamoto and Toshiharu Fujita, “Markov decision processes under fractional criterions,” Kyoto University RIMS Kokyuroku, no. 1079, pp. 153–163 (1999) (in Japanese).
[6] Krisorn Jittorntrum, “An implicit function theorem,” Journal of Optimization Theory and Applications, vol. 25, pp. 575–577 (1978).
[7] Hang-Chin Lai, “On a dynamic fractional game,” Kyoto University RIMS Kokyuroku, no. 1298, pp. 151–160 (2002).
[8] Hiroaki Morimoto, “On average cost stopping time problems,” Probability Theory and Related Fields, vol. 90, pp. 469–490 (1991).
[9] Masamitsu Ohnishi, “Optimal minimal-repair and replacement problem under average cost criterion: Optimality of(t,T)-policy,” Journal of the Operations Research Society of Japan, vol. 40, pp. 373–389 (1997).
[10] Martin L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming. New York, NY, USA: Wiley-Interscience (1994).
[11] Zhiyuan Ren and Bruce Krogh, “Markov decision processes with fractional costs,” IEEE Transactions on Automatic Control, vol. 50, pp. 646–650 (2005).
[12] Yoichi Sawasaki, Yutaka Kimura, and Kensuke Tanaka, “A two-person zero-sum game with fractional loss function,” Journal of the Operations Research Society of Japan, vol. 43, pp. 209–218 (2000).
[13] Maurice Robin, “On some impulse control problems with long run average cost,” SIAM Journal on Control and Optimization, vol. 19, pp. 333–358 (1981).
[14] Ioan Mihai Stancu-Minasian, Fractional Programming. Dordrecht, The Netherlands: Kluwer Academic Publishers (1997).
[15] Lukasz Stettner, “On some stopping impulse control problems with a general discount rate criteria,” Probability and Mathematical Statistics, vol. 10, pp. 223–245 (1989).
[16] Min Sun, “An optimal stopping time problem with time average cost in a bounded interval,” Systems & Control Letters, vol. 8, pp. 173–180 (1986).
[17] Min Sun, “A multidimensional optimal stopping-time problem with time-average criterion,” Optimal Control Applications and Methods, vol. 11, pp. 85–93 (1990).
[18] Teruo Tanaka, “A partially observable discrete-time Markov decision process with a fractional discounted reward,” Journal of Information and Optimization Sciences, vol. 38, no. 1, pp. 21–37 (2017).
[19] Qi Wang, Masayuki Kageyama, and Jingyao Zhang, “New evaluation criteria in the Markov decision processes,” Journal of Statistics and Management Systems, vol. 24, no. 3, pp. 625–632 (2021).




