Skip to main content
SpringerLink
Log in

Controlled diffusion processes on infinite horizon with the overtaking criterion

  • Published:
Applied Mathematics and Optimization Aims and scope Submit manuscript

Abstract

The optimal control of diffusion processes on the infinite time interval are studied. All the costs diverge to infinity and we employ the overtaking criterion, as well as considering minimal growth rate controls. The Bellman equation for the problem is considered and its solution is given an interpretation connected with the overtaking optimality notion. Control problems with a cost including a generalized discount factor (which is not integrable on [(, ∞)) are also studied. Both cases, where the diffusion is inR n or where it is reflected from the boundary of a bounded set, are considered.

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. Artstein Z, Leizarowitz A (1985) Tracking periodic signals with the overtaking criterion. IEEE Trans Autom Control 30:1123–1126

    Google Scholar 

  2. Aubin J-P, Cellina A (1984) Differential Inclusions. Springer-Verlag, New York

    Google Scholar 

  3. Bensoussan A, Lions J-L (1982) Impulse Control and Quasi-Variational Inequalities. Bordas, Paris

    Google Scholar 

  4. Gale, D (1967) On optimal development in a multi-sector economy. Rev Econom Stud 34:1–19

    Google Scholar 

  5. Has'minskii RZ (1980) Stochastic Stability of Differential Equations. Sijthoff and Noordhoff, Alphen aan den Rijn

    Google Scholar 

  6. Leizarowitz A (1985) Existence of overtaking optimal trajectories for problems with convex integrands. Math Oper Res 10:450–461

    Google Scholar 

  7. Leizarowitz, A (1985) Infinite horizong stochastic regulation and tracking with the overtaking criterion (to appear in Stochastics)

  8. Lions P-L, Trudinger NS (1986) Linear oblique derivative problem for the uniformly elliptic Hamilton-Jacobi-Bellman equation. Math Z 191:1–15

    Google Scholar 

  9. Lions P-L, Sznitman AS (1984) Stochastic differential equations with reflecting boundary conditions. Comm Pure Appl Math 37:511–537

    Google Scholar 

  10. Mendali J L, Robin M (1985) Construction and control of reflected diffusion with jumps. In: Thoma M (ed) Lecture Notes in Control and Information Sciences, vol 69

  11. Robin M (1983) Long-term average cost control problem for continuous time Markov processes: a survey. Acta Appl Math 1:281–299

    Google Scholar 

  12. Stroock DW, Varadhan SRS (1971) Diffusion processes with boundary conditions. Comm Pure Appl Math 24:147–225

    Google Scholar 

  13. von Weizsäcker CC (1965) Existence of optimal programs of accumulation for an infinite time horizon. Rev Econom Stud 32:85–164

    Google Scholar 

  14. Watanabe S (1971) On stochastic differential equations for multi-dimensional diffusion processes with boundary conditions. J Math Kyoto Univ 11:169–180

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

    Arie Leizarowitz

Authors
  1. Arie Leizarowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leizarowitz, A. Controlled diffusion processes on infinite horizon with the overtaking criterion. Appl Math Optim 17, 61–78 (1988). https://doi.org/10.1007/BF01448359

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01448359

Keywords

Search

Navigation