Skip to main content
SpringerLink
Log in

Some invariance principles for Stochastic processes and their inverse and supremum processes

  • Published:
Mathematische Zeitschrift 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. Bauer, H.: Invarianzprinzipien für Erneuerungsprozesse und ihre Verallgemeinerungen. Dissertation, Stuttgart, 1978

  2. Bauer, H.: On invariance principles with limit processes satisfying strong laws. To appear

  3. Billingsley, P.: Convergence of probability measures. New York: Wiley 1968

    Google Scholar 

  4. Bingham, N.H.: Limit theorems for regenerative phenomena, recurrent events and renewal theory. Z. Wahrscheinlichkeitstheorie verw. Gebiete21, 20–44 (1972)

    Google Scholar 

  5. Feller, W.: A limit theorem for random variables with infinite moments. Amer. J. Math.68, 257–262 (1946)

    Google Scholar 

  6. Feller, W.: An introduction to probability theory and its applications, Vol. II (2nd ed.). New York: Wiley 1971

    Google Scholar 

  7. Gut, A.: Weak convergence and first passage times. J. Appl. Probability12, 324–332 (1975)

    Google Scholar 

  8. Iglehart, D.L., Whitt, W.: The equivalence of functional central limit theorems for counting processes and associated partial sums. Ann. Math. Statist.42, 1372–1378 (1971)

    Google Scholar 

  9. Khintchine, A.: Zwei Sätze über stochastische Prozesse mit stabilen Verteilungen (Russian, with German summary). Mat. Sb. (N.S.)3 (45), 577–584 (1938)

    Google Scholar 

  10. Müller, D. W.: Verteilungsinvarianzprinzipien für das starke Gesetz der großen Zahl. Z. Wahrscheinlichkeitstheorie verw. Gebiete10, 173–192 (1968)

    Google Scholar 

  11. Sakhanenko, A.I.: The convergence of the distributions of functionals of processes that are defined on the whole axis. Siberian Math. J.15, 73–85 (1974)

    Google Scholar 

  12. Skorohod, A.V.: Limit theorems for stochastic processes with independent increments. Theor. Probability Appl.2, 138–171 (1957)

    Google Scholar 

  13. Vervaat, W.: Functional central limit theorems for processes with positive drift and their inverses. Z. Wahrscheinlichkeitstheorie verw. Gebiete23, 245–253 (1972)

    Google Scholar 

  14. Whitt, W.: Stochastic Abelian and Tauberian theorems. Z. Wahrscheinlichkeitstheorie verw. Gebiete22, 251–267 (1972)

    Google Scholar 

  15. Whitt, W.: Some useful functions for functional limit theorems. Math. Oper. Res.5, 67–85 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DFVLR, Rechenzentrum AMI, D-8031, Weßling, Bundesrepublik Deutschland

    Herbert Bauer

Authors
  1. Herbert Bauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was done in the Institute of Mathematics, University of Stuttgart.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bauer, H. Some invariance principles for Stochastic processes and their inverse and supremum processes. Math Z 175, 283–297 (1980). https://doi.org/10.1007/BF01163030

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01163030

Keywords

Search

Navigation