Theorem on the Structure of the Fractionally Linear Functional Extremal Function

Victor Kashtanov, Alexander Bochkov () and Olga Zaitseva ()
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Victor Kashtanov: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE), Federal State Autonomous Educational Institution for Higher Education, Higher School of Economics, National Research University, 101000 Moscow, Russia
Alexander Bochkov: JSC NIIAS, Research and Design Institute of Information, Automation and Communication on Railway Transport, 109029 Moscow, Russia
Olga Zaitseva: Moscow Aviation Institute, National Research University, 125993 Moscow, Russia

Mathematics, 2023, vol. 11, issue 13, 1-14

Abstract: The paper proves a theorem about the structure of the distribution function on which the extremum of the fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters; hence, the problem is greatly simplified since it is reduced to the search for an extremum of some function.

Keywords: distribution function; extremum; fractionally linear functional; stochastic models; controllable semi-Markov process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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