Skip to main content
Log in

Revuz Measures and Related Formulas on Energy Functional and Capacity

  • Published:
Potential Analysis Aims and scope Submit manuscript

Abstract

In the context of right Markov processes, Revuz measures of additive and multiplicative functionals are investigated. Using Revuz measures, several formulas on the energy functional and capacity are given to describe the relationships between any process and its subprocesses.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Blumenthal, R. M. and Getoor, R. K.: Markov Processes and Potential Theory, Academic Press, New York, 1968.

    Google Scholar 

  2. Fitzsimmons, P.J. and Maisonneuve, B.: ‘Excessive measures and Markov processes with random birth and death’, Probab. Th. Rel. Fields 72 (1986), 319-336.

    Google Scholar 

  3. Fitzsimmons, P. J. and Getoor, R. K.: Some formulas for the energy functional of a Markov process, Seminar on Stochastic Processes 1988 (1989), 161-182.

  4. Fitzsimmons, P.J. and Getoor, R.K.: ‘Revuz measures and time changes’, Math. Zeit. 199 (1988), 233-256.

    Google Scholar 

  5. Getoor, R. K.: Excessive Measures, Birkhauser, 1990.

  6. Getoor, R. K.: ‘Killing a Markov process under a stationary measure involves creation’, Ann. Probab., V.162 (1988), 564-585.

    Google Scholar 

  7. Getoor, R. K. and Steffens, J.: ‘The energy functional, balayage, and capacity’, Ann. Inst. Henri Poincaré 23 (1987) 321-357.

    Google Scholar 

  8. Getoor, R. K. and Steffens, J.: More about capacity and excessive measures, Seminar on Stochastic Processes 1987 (1988) 135-157.

  9. Revuz, D.: ‘Mesures associées aux fonctionnelles additives de Markov I’, Trans. Amer. Math. Soc. 148 (1970), 501-531.

    Google Scholar 

  10. Revuz, D.: ‘Mesures associées aux fonctionnelles additives de Markov II’, Z.W. 16 (1970), 336-344.

    Google Scholar 

  11. Sharpe, M. J.: General Theory of Markov Processes, Academic Press, 1988.

  12. Toby, E.: Birth and death of a Markov process under a stationary measure, Ph.D. Thesis, UC San Diego, 1988.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ying, J. Revuz Measures and Related Formulas on Energy Functional and Capacity. Potential Analysis 8, 1–19 (1998). https://doi.org/10.1023/A:1017966116127

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1017966116127

Navigation