Skip to main content

An Elementary Proof that the First Hitting Time of an Open Set by a Jump Process is a Stopping Time

  • Chapter
  • First Online:
Book cover Séminaire de Probabilités XLV

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2078))

Abstract

We give a short and elementary proof that the first hitting time of an open set by the jump process of a càdlàg adapted process is a stopping time.

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.F. Bass, The measurability of hitting times. Electron. Comm. Probab. 15, 99–105 (2010)

    MathSciNet  MATH  Google Scholar 

  2. R.F. Bass, Correction to “The measurability of hitting times”. Electron. Comm. Probab. 16, 189–191 (2011)

    MathSciNet  MATH  Google Scholar 

  3. C. Dellacherie, P.-A. Meyer, Probabilities and Potential. North-Holland Mathematics Studies, vol. 29 (North-Holland, Amsterdam, 1978)

    Google Scholar 

  4. P. Protter, Stochastic Integration and Differential Equations, 2nd edn. Version 2.1. Stochastic Modelling and Applied Probability, vol. 21 (Springer, Berlin, 2005)

    Google Scholar 

  5. L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, 2nd edn., vol. 1 (Cambridge University Press, Cambridge, 2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander Sokol .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Sokol, A. (2013). An Elementary Proof that the First Hitting Time of an Open Set by a Jump Process is a Stopping Time. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLV. Lecture Notes in Mathematics(), vol 2078. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00321-4_11

Download citation

Publish with us

Policies and ethics