Skip to main content
SpringerLink
Log in

On the spectrum of a class of matrices arising in storage theory

  • Published:
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete Aims and scope Submit manuscript

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

References

  1. Brockwell, P.J.: A storage model in which the net growth-rate is a Markov chain. J. Appl. Probab. 9, 129–139 (1972).

    Google Scholar 

  2. Erickson, R.V.: Stationary measures for a class of storage models driven by a Markov chain. Ann. Math. Statistics 43, 997–1007 (1972).

    Google Scholar 

  3. Feller, W.: An Introduction to Probability Theory and its Applications, Vol. 2, 2nd ed. New York: John Wiley and Sons Inc. 1971.

    Google Scholar 

  4. Keilson, J., Subba Rao, S.: A process with chain-dependent growth-rate. Part II. The ruin and ergodic problems. Advances Appl. Probab. 3, 315–338 (1971).

    Google Scholar 

  5. Miller, R.G., Jr.: Continuous time stochastic storage processes with random linear inputs and outputs. J. Math. Mech. 12, 275–291 (1963).

    Google Scholar 

  6. Pinsky, M.: Multiplicative operator functionals and their asymptotic properties. Advances in Probab. (To appear.)

  7. Pyke, R.: On renewal processes related to Type I and Type II counter models. Ann. Math. Statistics 29, 737–754 (1958).

    Google Scholar 

  8. Weldon, K.L.M.: Stochastic storage processes with multiple slope linear inputs and outputs. Tech. Report No. 9, Statistics Department, Stanford University, August 1969.

  9. Wilkinson, J.H.: The Algebraic Eigenvalue Problem. Oxford: Clarendon Press 1965.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Michigan State University, 48823, East Lansing, Michigan, USA

    P. J. Brockwell

Authors
  1. P. J. Brockwell
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work partially supported by United States Air Force Contract F44620-67-C-0049 while the author was in the Department of Mathematics, Stanford University.

I am indebted to the referee for a number of helpful comments which led to improvements in the presentation of the results.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brockwell, P.J. On the spectrum of a class of matrices arising in storage theory. Z. Wahrscheinlichkeitstheorie verw Gebiete 25, 253–260 (1973). https://doi.org/10.1007/BF00535896

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00535896

Keywords

Search

Navigation