Skip to main content

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2137))

Abstract

The goal of this paper is to define and study loop measures for Markov processes without transition densities. In particular, we prove the shift invariance of the based loop measure.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. R. Blumenthal, R. Getoor, Markov Processes and Potential Theory (Academic, New York, 1968)

    MATH  Google Scholar 

  2. D. Brydges, J. Fröhlich, T. Spencer, The random walk representation of classical spin systems and correlation inequalities. Commun. Math. Phys. 83(1), 123–150 (1982)

    Article  Google Scholar 

  3. C. Dellacherie, P.-A. Meyer, Probabilities and Potential B (North Holland, Amsterdam, 1982)

    MATH  Google Scholar 

  4. P. Fitzsimmons, R.K. Getoor, Homogeneous random measures and strongly supermedian kernels of a Markov process. Electron. J. Probab. 8, 1–54 (2003)

    Article  MathSciNet  Google Scholar 

  5. P.J. Fitzsimmons, J. Rosen, Markovian loop soups: permanental processes and isomorphism theorems. Electron. J. Probab. 19(60), 1–30 (2014)

    MathSciNet  Google Scholar 

  6. R.K. Getoor, J. Glover, Constructing Markov processes with random times of birth and death. Seminar on Stochastic Processes, 1986, ed. by E. Cinlar, K.L. Chung, R.K. Getoor, J. Glover, Progress in Probability and Statistics, vol. 13 (Birkhäuser, Boston, 1987), pp. 35–69

    Google Scholar 

  7. G. Lawler, W. Werner, The Brownian loop soup. Probab. Theory Relat. Fields 44, 197–217 (2004)

    MathSciNet  Google Scholar 

  8. Y. Le Jan, Markov Paths, Loops and Fields. École d’Été de Probabilités de Saint-Flour XXXVIII - 2008. Lecture Notes in Mathematics, vol. 2026 (Springer, Berlin, 2011)

    Google Scholar 

  9. Y. Le Jan, M.B. Marcus, J. Rosen, Permanental fields, loop soups and continuous additive functionals. Ann. Probab. 43(1), 44–84 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  10. Y. Le Jan, M.B. Marcus, J. Rosen, Intersection local times, loop soups and permanental Wick powers. http://arxiv.org/pdf/1308.2701.pdf

  11. M. Sharpe, General Theory of Markov Processes (Academic, New York, 1988)

    MATH  Google Scholar 

  12. K. Symanzyk, Euclidean quantum field theory, in Local Quantum Theory, ed. by R. Jost (Academic, Reading, 1969)

    Google Scholar 

Download references

Acknowledgements

Research of J. Rosen was partially supported by grants from the National Science Foundation and PSC CUNY.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yves Le Jan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Fitzsimmons, P., Jan, Y.L., Rosen, J. (2015). Loop Measures Without Transition Probabilities. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) In Memoriam Marc Yor - Séminaire de Probabilités XLVII. Lecture Notes in Mathematics(), vol 2137. Springer, Cham. https://doi.org/10.1007/978-3-319-18585-9_14

Download citation

Publish with us

Policies and ethics