Skip to main content
SpringerLink
Log in

Birth and Death on a Flow: Local Time and Estimation of a Position‐Dependent Death Rate

  • Published:
Statistical Inference for Stochastic Processes Aims and scope Submit manuscript

Abstract

The paper deals with statistical inference for an unknown rate of position‐dependent killing in birth and death on a flow. We introduce local time for this process and discuss its asymptotics with the help of a Tanaka formula. As a consequence, we can prove asymptotic normality of kernel estimators for the death rate.

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. Çinlar, E. and Kao, J. S.: Birth and death on a flow, in X. Pinsky and Y. Wihstutz (eds), Diffusion Processes and Related Topics (Proc. 1989), Vol. 2, Stochastic Flows, Birkhäuser, Boston, 1992, pp. 121-137.

    Google Scholar 

  2. Höpfner, R. and Löcherbach, E.: On statistical models for birth and death on a flow: local asymptotic continuity and likelihood ratio processes. Scand. J. Statist 26 (1999), 107-128.

    Article  MATH  MathSciNet  Google Scholar 

  3. Höpfner, R. and Löcherbach, E.: On local asymptotic normality for birth and death on a flow. Stoch. Proc. Appl 83, 61-78 (1999).

    Article  MATH  Google Scholar 

  4. Jacod, J. and Shiryaev, A. N.: Limit Theorem for Stochastic Processes, Springer, Berlin, 1987.

    Google Scholar 

  5. Karatzas, I. and Shreve, S. E.: Brownian Motion and Stochastic Calculus, 2nd edn, Springer, New York, 1991.

    Google Scholar 

  6. Kunita, H.: Stochastic Flows and Stochastic Differential Equation, Cambridge University Press, Cambridge, 1992.

    Google Scholar 

  7. Kutoyants, Yu: Efficient density estimation for ergodic diffusion processes, Statistic. Inference for Stoch. Processes (to appear).

  8. Phelan, M. J.: Asymptotic likelihood estimation from birth and death on a flow. Ann. Statist. 24 (1996), 1161-1184.

    Article  MATH  MathSciNet  Google Scholar 

  9. Phelan, M. J.: A Girsanov transformation for birth and death on a Brownian flow. J. Appl. Probab. 33 (1996), 88-100.

    Article  MATH  MathSciNet  Google Scholar 

  10. Phelan, M. J.: Approach to stationarity for birth and death on flows. Stoch. Proc. Appl. 66 (1997), 183-207.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität Mainz, Fachbereich 17 Mathematik, Staudinger Weg 9, 55099, Mainz, Germany

    R. HÖpfner & E. LÖcherbach

Authors
  1. R. HÖpfner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. LÖcherbach
    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

HÖpfner, R., LÖcherbach, E. Birth and Death on a Flow: Local Time and Estimation of a Position‐Dependent Death Rate. Statistical Inference for Stochastic Processes 1, 225–243 (1998). https://doi.org/10.1023/A:1009944302344

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009944302344

Search

Navigation