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This article is cited in 2 scientific papers (total in 2 papers)
On the existence of a solution in a problem of controlling a counting process
Yu. M. Kabanov
Abstract:
An existence theorem is proved in the control problem $\mathbf E^u\xi\to\max$, where $\xi$ is a bounded functional of the sample functions of a counting process $x=(x_t)_{t\geqslant0}$ with intensity $\lambda^u=\lambda(x,t,u(x,t))$. It is assumed that $\xi$ satisfies a certain condition of weak dependence on the “tail” of the sample function. The proof is based on compactness considerations and makes essential use of a description of the extreme points of the set of admissible local densities. The Appendix gives a description of the set of extreme points for the family of distribution densities of diffusion-type processes relative to Wiener measure.
Bibliography: 17 titles.
Received: 09.04.1981
Citation:
Yu. M. Kabanov, “On the existence of a solution in a problem of controlling a counting process”, Mat. Sb. (N.S.), 119(161):3(11) (1982), 431–445; Math. USSR-Sb., 47:2 (1984), 425–438
Linking options:
https://www.mathnet.ru/eng/sm2895https://doi.org/10.1070/SM1984v047n02ABEH002653 https://www.mathnet.ru/eng/sm/v161/i3/p431
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Abstract page: | 302 | Russian version PDF: | 89 | English version PDF: | 5 | References: | 52 |
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