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 Mat. Sb. (N.S.), 1982, Volume 119(161), Number 3(11), Pages 431–445 (Mi msb2895)

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.

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English version:
Mathematics of the USSR-Sbornik, 1984, 47:2, 425–438

Bibliographic databases:

UDC: 519.21
MSC: Primary 49A60, 93E20; Secondary 60E99, 60G55, 60J60

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

Citation in format AMSBIB
\Bibitem{Kab82} \by Yu.~M.~Kabanov \paper On~the existence of a solution in a problem of controlling a~counting process \jour Mat. Sb. (N.S.) \yr 1982 \vol 119(161) \issue 3(11) \pages 431--445 \mathnet{http://mi.mathnet.ru/msb2895} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=678839} \zmath{https://zbmath.org/?q=an:0536.49005} \transl \jour Math. USSR-Sb. \yr 1984 \vol 47 \issue 2 \pages 425--438 \crossref{https://doi.org/10.1070/SM1984v047n02ABEH002653} 

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This publication is cited in the following articles:
1. Delbaen F., “The Structure of M-Stable Sets and in Particular of the Set of Risk Neutral Measures”, In Memoriam Paul-Andre Meyer: Seminaire de Probabilities Xxxix, Lecture Notes in Mathematics, 1874, eds. Emery M., Yor M., Springer-Verlag Berlin, 2006, 215–258
2. Birger Wernerfelt, “On Existence of a nash equilibrium point in N-person non-zero sum stochastic jump differential games”, Optim Control Appl Meth, 9:4 (2007), 449
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