On the Existence of the Optimal Control for Stochastic Functional Differential Equations Subject to External Disturbances

The authors discuss the comparison theorem for solutions of stochastic functional differential equations subject to external disturbances and its application to a stochastic control problem. Keywords: comparison theorem, stochastic control, stochastic functional differential equations.

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Published in	Cybernetics and systems analysis Vol. 60; no. 3; pp. 462 - 471
Main Authors	Yasynskyy, V. K., Yurchenko, I. V.
Format	Journal Article
Language	English
Published	New York Springer US 01.05.2024 Springer Springer Nature B.V
Subjects	Analysis Artificial Intelligence Control Control systems Differential equations Disturbances Investment analysis Mathematics Mathematics and Statistics Optimal control Processor Architectures Software Engineering/Programming and Operating Systems Stochastic processes Systems Theory stochastic functional differential equations stochastic control comparison theorem
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Abstract	The authors discuss the comparison theorem for solutions of stochastic functional differential equations subject to external disturbances and its application to a stochastic control problem. Keywords: comparison theorem, stochastic control, stochastic functional differential equations.
AbstractList	The authors discuss the comparison theorem for solutions of stochastic functional differential equations subject to external disturbances and its application to a stochastic control problem. The authors discuss the comparison theorem for solutions of stochastic functional differential equations subject to external disturbances and its application to a stochastic control problem. Keywords: comparison theorem, stochastic control, stochastic functional differential equations.
Audience	Academic
Author	Yurchenko, I. V. Yasynskyy, V. K.
Author_xml	– sequence: 1 givenname: V. K. surname: Yasynskyy fullname: Yasynskyy, V. K. email: v.yasynskyy@chnu.edu.ua organization: Yuriy Fedkovych Chernivtsi National University – sequence: 2 givenname: I. V. surname: Yurchenko fullname: Yurchenko, I. V. organization: Yuriy Fedkovych Chernivtsi National University
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References	GikhmanIISkorokhodAVStochastic Differential Equations1968KyivNaukova Dumka[in Russian] K. J. Aström, Introduction to Stochastic Control Theory, Dover Publ. (2006). R. Bellman, “Dynamic programming and stochastic control processes,” Information and Control, Vol. 1, Iss. 3, 228–239 (1958). https://doi.org/10.1016/S0019-9958(58)80003-0. I. V. Yurchenko, “The comparison theorem for the solution of the stochastic differential functional equations,” in: Proc. Intern. Math. Conf. Dedicated to Hans Hahn, Ruta, Chernivtsi (1995), pp. 322–332. KnopovPSOptimization and identification of stochastic systemsCybern. Syst. Analysis2023593375384458550110.1007/s10559-023-00572-4 GikhmanIISkorokhodAVStochastic Differential Equations and their Application1982KyivNaukova Dumka[in Russian] ShigaTokuzoDiffusion processes in population geneticsJ. Math. Kyoto Univ.1981211133151606316 IkedaNWatanabeSStochastic Differential Equations and Diffusion Processes1989AmsterdamNorth-Holland Mathematical Library V. K. Yasynskyy and I. V. Yurchenko, Stability and Optimal Control in Stochastic Dynamic Systems with Random Operators [in Ukrainian], Tekhnoprint, Chernivtsi (2019). B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, Springer Science+Business Media, Heidelberg–New York–Dordrecht–London (2013). https://doi.org/10.1007/978-3-642-14394-6. M. L. Sverdan, E. F. Tsarkov, and V. K. Yasynskyy, Stability in the Stochastic Modeling of Complex Dynamic Systems [in Ukrainian], Nad Prutom, Sniatyn (1996). KolmanovskiiVBShaikhetLE“One method of constructing an approximate synthesis of optimal control”, Dopovidi AN UkrRSRSer. A, No.197883236 V. K. Yasyns’kyi, M. L. Sverdan, and I. V. Yurchenko, “On one problem of stochastic control,” Ukr. Math. J., Vol. 47, No. 11, 1788–1797 (1995). https://doi.org/10.1007/BF01057927. E. F. Tsarkov and V. K. Yasynskyy, Quasilinear Stochastic Differential Equations [in Russian], Orientir, Riga (1992). YamadaToshioOn a comparison theorem for solutions of stochastic differential equations and its applicationsJ. Math. Kyoto Univ.197313349751233933410.1215/kjm/1250523321 VB Kolmanovskii (687_CR4) 1978; 8 II Gikhman (687_CR3) 1982 Toshio Yamada (687_CR5) 1973; 13 687_CR11 687_CR10 687_CR13 687_CR1 687_CR12 687_CR15 687_CR14 687_CR9 N Ikeda (687_CR7) 1989 PS Knopov (687_CR8) 2023; 59 Tokuzo Shiga (687_CR6) 1981; 21 II Gikhman (687_CR2) 1968
References_xml	– reference: GikhmanIISkorokhodAVStochastic Differential Equations and their Application1982KyivNaukova Dumka[in Russian] – reference: R. Bellman, “Dynamic programming and stochastic control processes,” Information and Control, Vol. 1, Iss. 3, 228–239 (1958). https://doi.org/10.1016/S0019-9958(58)80003-0. – reference: V. K. Yasyns’kyi, M. L. Sverdan, and I. V. Yurchenko, “On one problem of stochastic control,” Ukr. Math. J., Vol. 47, No. 11, 1788–1797 (1995). https://doi.org/10.1007/BF01057927. – reference: IkedaNWatanabeSStochastic Differential Equations and Diffusion Processes1989AmsterdamNorth-Holland Mathematical Library – reference: I. V. Yurchenko, “The comparison theorem for the solution of the stochastic differential functional equations,” in: Proc. Intern. Math. Conf. Dedicated to Hans Hahn, Ruta, Chernivtsi (1995), pp. 322–332. – reference: GikhmanIISkorokhodAVStochastic Differential Equations1968KyivNaukova Dumka[in Russian] – reference: ShigaTokuzoDiffusion processes in population geneticsJ. Math. Kyoto Univ.1981211133151606316 – reference: YamadaToshioOn a comparison theorem for solutions of stochastic differential equations and its applicationsJ. Math. Kyoto Univ.197313349751233933410.1215/kjm/1250523321 – reference: V. K. Yasynskyy and I. V. Yurchenko, Stability and Optimal Control in Stochastic Dynamic Systems with Random Operators [in Ukrainian], Tekhnoprint, Chernivtsi (2019). – reference: B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, Springer Science+Business Media, Heidelberg–New York–Dordrecht–London (2013). https://doi.org/10.1007/978-3-642-14394-6. – reference: K. J. Aström, Introduction to Stochastic Control Theory, Dover Publ. (2006). – reference: M. L. Sverdan, E. F. Tsarkov, and V. K. Yasynskyy, Stability in the Stochastic Modeling of Complex Dynamic Systems [in Ukrainian], Nad Prutom, Sniatyn (1996). – reference: KnopovPSOptimization and identification of stochastic systemsCybern. Syst. Analysis2023593375384458550110.1007/s10559-023-00572-4 – reference: E. F. Tsarkov and V. K. Yasynskyy, Quasilinear Stochastic Differential Equations [in Russian], Orientir, Riga (1992). – reference: KolmanovskiiVBShaikhetLE“One method of constructing an approximate synthesis of optimal control”, Dopovidi AN UkrRSRSer. A, No.197883236 – ident: 687_CR11 – volume: 8 start-page: 32 year: 1978 ident: 687_CR4 publication-title: Ser. A, No. – ident: 687_CR14 – ident: 687_CR12 – ident: 687_CR15 – ident: 687_CR1 doi: 10.1016/S0019-9958(58)80003-0 – volume-title: Stochastic Differential Equations and Diffusion Processes year: 1989 ident: 687_CR7 – volume-title: Stochastic Differential Equations year: 1968 ident: 687_CR2 – ident: 687_CR9 – ident: 687_CR10 doi: 10.1007/978-3-642-14394-6 – ident: 687_CR13 doi: 10.1007/BF01057927 – volume: 13 start-page: 497 issue: 3 year: 1973 ident: 687_CR5 publication-title: J. Math. Kyoto Univ. doi: 10.1215/kjm/1250523321 – volume: 59 start-page: 375 issue: 3 year: 2023 ident: 687_CR8 publication-title: Cybern. Syst. Analysis doi: 10.1007/s10559-023-00572-4 – volume: 21 start-page: 133 issue: 1 year: 1981 ident: 687_CR6 publication-title: J. Math. Kyoto Univ. – volume-title: Stochastic Differential Equations and their Application year: 1982 ident: 687_CR3
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SubjectTerms	Analysis Artificial Intelligence Control Control systems Differential equations Disturbances Investment analysis Mathematics Mathematics and Statistics Optimal control Processor Architectures Software Engineering/Programming and Operating Systems Stochastic processes Systems Theory
Title	On the Existence of the Optimal Control for Stochastic Functional Differential Equations Subject to External Disturbances
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