Skip to main content
SpringerLink
Log in

A Remark on the Characterization of the Global Behavior of a Process with Independent Increments

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We show that the analysis of the global behavior of a process with independent increments in terms of the existence of the stationary distribution of the corresponding storage process leads to results that differ from the classical ones.

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. A. V. Skorokhod, Random Processes with Independent Increments[in Russian], Nauka, Moscow (1964).

    Google Scholar 

  2. P. J. Brockwell, “Stationary distributions for dams with additive input and content-dependent release rule,” Adv. Appl. Probab., 9, No.3, 645–663 (1977).

    Google Scholar 

  3. P. J. Brockwell and K. L. Chung, “Emptiness times of a dam with stable input and general release rule,” J. Appl. Probab., 12, No.1, 212–217 (1975).

    Google Scholar 

  4. P. J. Brockwell, S. I. Resnick, and R. L. Tweedie, “Storage processes with general release rule and additive inputs,” Adv. Appl. Probab., 14, No.2, 392–433 (1982).

    Google Scholar 

  5. E. Cinlar and M. Pinsky, “A stochastic integral in storage theory,” Z. Wahrscheinlichkeitstheor. Verw. Geb., 17, No.3, 227–240 (1971).

    Google Scholar 

  6. E. Cinlar and M. Pinsky, “On dams with additive inputs and a general release rule,” J. Appl. Probab., 9, No.2, 422–429 (1972).

    Google Scholar 

  7. J. M. Harrison and S. I. Resnick, “The stationary distribution and first exit probabilities of a storage process with general release rule,” Math. Oper. Res., 1, No.4, 347–358 (1976).

    Google Scholar 

  8. P. A. P. Moran, “A theory of dams with continuous input and a general release rule,” J. Appl. Probab., 6, No.1, 88–98 (1969).

    Google Scholar 

  9. M. Rubinovich and J. W. Cohen, “Level crossings and stationary distributions for general dams,” J. Appl. Probab., 17, No.1, 218–226 (1980).

    Google Scholar 

  10. O. K. Zakusilo, “General storage processes with additive inputs,” Teor. Ver. Primen., 34, Issue 2, 277–288 (1989).

    Google Scholar 

  11. O. K. Zakusilo, “On limit characteristics of certain Markov processes with deterministic drift,” Teor. Ver. Mat. Statist., Issue 34, 53–61 (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev University, Kiev

    O. K. Zakusilo

Authors
  1. O. K. Zakusilo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zakusilo, O.K. A Remark on the Characterization of the Global Behavior of a Process with Independent Increments. Ukrainian Mathematical Journal 52, 1380–1382 (2000). https://doi.org/10.1023/A:1010323901452

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010323901452

Keywords

Search

Navigation