Hostname: page-component-6bf8c574d5-8gtf8 Total loading time: 0 Render date: 2025-02-17T16:22:49.208Z Has data issue: false hasContentIssue false
  • English
  • Français

On the optimal control of stationary diffusion processes with inaccessible boundaries and no discounting

Published online by Cambridge University Press:  14 July 2016

R. Morton
R. Morton*
Affiliation:
University of Manchester
Get access Rights & Permissions [Opens in a new window]

Summary

Because there are no boundary conditions, extra properties are required in order to identify the correct potential cost function. A solution of the Dynamic Programming equation for one-dimensional processes leads to an optimal solution within a wide class of alternatives (Theorem 1), and is completely optimal if certain conditions are satisfied (Theorem 2). Necessary conditions are also given. Several examples are solved, and some extension to the multidimensional case is shown.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 3 , September 1971 , pp. 551 - 560
Copyright
Copyright © Applied Probability Trust 1971 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Aoki, M. (1967) Optimisation of Stochastic Systems. Academic Press, New York and London.Google Scholar
[2] Bather, J. A. (1969) Diffusion models in stochastic control theory. J. R. Statist. Soc. A 132, 335–345.Google Scholar
[3] Derman, C. and Veinott, A. F. (1967) A solution to a countable system of equations arising in Markov decision processes. Ann. Math. Statist. 38, 582–585.Google Scholar
[4] Fleming, W. H. (1966) Optimal control of diffusion processes. Functional Analysis and Optimisation, 67–84, Academic Press, New York.Google Scholar
[5] Fleming, W. H. and Nisio, M. (1966) On the existence of optimal stochastic controls. J. Math. Mech. 15, 777–794.Google Scholar
[6] Howard, R. A. (1960) Dynamic Programming and Markov Processes. M.I.T. Press, Cambridge, Mass.Google Scholar
[7] Kogan, Ya. A. (1969) On optimal control of a non-terminating diffusion process with reflection. Theor. Probability Appl. 14, 496–502.CrossRefGoogle Scholar
[8] Mandl, P. (1964) On the control of a non-terminating diffusion process. Theor. Probability Appl. 9, 591–603.Google Scholar
[9] Mandl, P. (1965) On optimal control of non-stopped diffusion processes. Z. Wahrscheinlichkeitsth. 4, 1–9.CrossRefGoogle Scholar
[10] Mandl, P. (1965) Analytic methods in the theory of controlled Markov processes. Trans. 4th Prague Conf. on Inf. Th., etc. 45–53.Google Scholar
[11] Mandl, P. (1968) Analytical Treatment of One-Dimensional Markov Processes, Academia, Prague, and Springer-Verlag, Berlin.Google Scholar