A. Ya. Kogan, “On optimal control of a non-stopped diffusion process with reflection”, Teor. Veroyatnost. i Primenen., 14:3 (1969), 516–522; Theory Probab. Appl., 14:3 (1969), 496

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Teoriya Veroyatnostei i ee Primeneniya, 1969, Volume 14, Issue 3, Pages 516–522 (Mi tvp1206)

This article is cited in 14 scientific papers (total in 14 papers)

Short Communications

On optimal control of a non-stopped diffusion process with reflection

A. Ya. Kogan

Moscow

Full-text PDF (453 kB) Citations (14)

Abstract: In the paper the results of [1] are generalized to the multi-dimensional case, when boundary conditions are reduced to reflection in a non-tangential direction $\gamma$. It is supposed that the drift coefficients only are controllable. The method proposed to prove Theorem 1 gives a more effective procedure of finding the optimal value of the performance $\widehat\theta$ than that in [1].

Received: 05.04.1968

English version:
Theory of Probability and its Applications, 1969, Volume 14, Issue 3, Pages 496–502
DOI: https://doi.org/10.1137/1114063

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. Ya. Kogan, “On optimal control of a non-stopped diffusion process with reflection”, Teor. Veroyatnost. i Primenen., 14:3 (1969), 516–522; Theory Probab. Appl., 14:3 (1969), 496–502

Citation in format AMSBIB

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\by A.~Ya.~Kogan

\paper On optimal control of a~non-stopped diffusion process with reflection

\jour Teor. Veroyatnost. i Primenen.

\yr 1969

\vol 14

\issue 3

\pages 516--522

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\zmath{https://zbmath.org/?q=an:0214.16802|0214.16704}

\transl

\jour Theory Probab. Appl.

\yr 1969

\vol 14

\issue 3

\pages 496--502

\crossref{https://doi.org/10.1137/1114063}

Linking options:

https://www.mathnet.ru/eng/tvp1206

https://www.mathnet.ru/eng/tvp/v14/i3/p516

Erratum

Letter to the editors
A. Ya. Kogan
Teor. Veroyatnost. i Primenen., 1970, 15:1, 171

This publication is cited in the following 14 articles:

Beatris Adriana Escobedo-Trujillo, José Daniel López-Barrientos, Javier Garrido-Meléndez, “A Constrained Markovian Diffusion Model for Controlling the Pollution Accumulation”, Mathematics, 9:13 (2021), 1466
J. -L. Menaldi, M. Robin, “Ergodic control of reflected diffusions with jumps”, Appl Math Optim, 35:2 (1997), 117
Arie Leizarowitz, “Optimal controls for diffusion in Rd—A min-max max-min formula for the minimal cost growth rate”, Journal of Mathematical Analysis and Applications, 149:1 (1990), 180
T. Bielecki, ?. Stettner, “On ergodic control problems for singularly perturbed Markov processes”, Appl Math Optim, 20:1 (1989), 131
T. Bielecki, Ł. Stettner, Lecture Notes in Control and Information Sciences, 136, Stochastic Systems and Optimization, 1989, 274
Arie Leizarowitz, “On almost sure optimization for stochastic control systems”, Stochastics, 23:2 (1988), 85
A. Bensoussan, G. L. Blankenship, Lecture Notes in Control and Information Sciences, 90, Singular Perturbations and Asymptotic Analysis in Control Systems, 1987, 171
Maurice Robin, “Long-term average cost control problems for continuous time Markov processes: A survey”, Acta Appl Math, 1:3 (1983), 281
Maurice Robin, “On Some Impulse Control Problems with Long Run Average Cost”, SIAM J. Control Optim., 19:3 (1981), 333
N. El Karoui, Lecture Notes in Mathematics, 876, Ecole d'Eté de Probabilités de Saint-Flour IX-1979, 1981, 73
H. J. Kushner, “Optimality Conditions for the Average Cost per Unit Time Problem with a Diffusion Model”, SIAM J. Control Optim., 16:2 (1978), 330
M. L. Puterman, “Optimal control of diffusion processes with reflection”, J Optim Theory Appl, 22:1 (1977), 103
R. Morton, “On the optimal control of stationary diffusion processes with inaccessible boundaries and no discounting”, Journal of Applied Probability, 8:3 (1971), 551
R. Morton, “On the optimal control of stationary diffusion processes with inaccessible boundaries and no discounting”, J. Appl. Probab., 8:03 (1971), 551

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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