Abstract
This paper focuses on optimal control of nonlinear stochastic delay system constructed through Teugels martingales associated with Lévy processes and standard Brownian motion, in which finite horizon is extended to infinite horizon. In order to describe the interacting many-body system, the expectation values of state processes are added to the concerned system. Further, sufficient and necessary conditions are established under convexity assumptions of the control domain. Finally, an example is given to demonstrate the application of the theory.
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The author would like to thank the editor, the associate editor and anonymous referees for their constructive corrections and valuable suggestions that improved the manuscript.
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This work was supported by Science Engineering Research Board (SERB), DST, Govt. of India under YSS Project F. No: YSS/2014/000447 dated 20.11.2015. The second author is thankful to UGC, New Delhi, for providing BSR fellowship for the year 2015.
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Muthukumar, P., Deepa, R. Mean-Field, Infinite Horizon, Optimal Control of Nonlinear Stochastic Delay System Governed by Teugels Martingales Associated with Lévy Processes. Commun. Math. Stat. 7, 163–180 (2019). https://doi.org/10.1007/s40304-018-0143-z
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DOI: https://doi.org/10.1007/s40304-018-0143-z
Keywords
- Backward stochastic delay differential equation
- Infinite horizon
- Lévy processes
- Mean-field
- Stochastic maximum principle
- Teugels martingales