Skip to main content
SpringerLink
Log in

Single-person controlled diffusions with discounted costs

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper describes a class of single-person controlled one-dimensional diffusion processes where the control is a vector-valued function on the state space, which is a compact interval of the real line. These processes generate costs, and the optimal control problem is to choose an admissible control that minimizes expected discounted costs. The major results are necessary and sufficient conditions for a control to be optimal as well as characterizations of the expected costs corresponding to an optimal control. This paper also established sufficient conditions for the existence of piecewise-continuous optimal controls.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Mandl, P.,Analytical Treatment of One-Dimensional Markov Processes, Springer-Verlag, New York, New York, 1968.

    MATH  Google Scholar 

  2. Pliska, S.,Multi-Person Controlled Diffusions, SIAM Journal on Control (to appear).

  3. Pliska, S.,Single and Multi-Person Controlled Diffusions, Stanford University, Department of Operations Research, Technical Report No. 23, 1972.

  4. Halkin, H.,A Generalization of LaSalle's Bang-bang Principle, SIAM Journal on Control, Vol. 2, No. 2, 1964.

  5. Fleming, W. H.,Duality and a Priori Estimates in Markovian Optimization Problems, Journal of Mathematical Analysis and Applications, Vol. 16, No. 2, 1966.

  6. Berge, C.,Topological Spaces, Oliver Boyd, London, England, 1963.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois

    S. R. Pliska (Assistant Professor)

Authors
  1. S. R. Pliska
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by L. D. Berkovitz

The author is grateful to M. L. Puterman and R. W. Rosenthal for their helpful comments during the course of this research. The author is especially indebted to A. F. Veinott, Jr., for his guidance of the author's doctoral dissertation, on part of which this paper is based. This research was supported by the National Science Foundation, Grant No. GK-18339, as well as the Office of Naval Research, Contract No. N00014-67-A-0112-0050.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pliska, S.R. Single-person controlled diffusions with discounted costs. J Optim Theory Appl 12, 248–255 (1973). https://doi.org/10.1007/BF00935107

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00935107

Keywords

Search

Navigation