Skip to main content
SpringerLink
Log in

On the Successive Passage Times of Certain One-Dimensional Diffusions

  • Conference paper
  • First Online:
Computer Aided Systems Theory – EUROCAST 2019 (EUROCAST 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12013))

Included in the following conference series:

  • 796 Accesses

Abstract

We study the distribution of the nth-passage time of a one-dimensional diffusion, obtained by a space or time transformation of Brownian motion, through a constant barrier a. Some explicit examples are reported.

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

Access this chapter

Log in via an institution
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. Abundo, M., Scioscia Santoro, M.B.: On the successive passage times of certain one-dimensional diffusions. Preprint 2018 arXiv:1803.09910 (2018)

  2. Abundo, M.: On the excursions of drifted Brownian motion and the successive passage times of Brownian motion. Physica A 457, 176–182 (2016). https://doi.org/10.1016/j.physa.2016.03.052

    Article  MathSciNet  MATH  Google Scholar 

  3. Abundo, M.: On the representation of an integrated Gauss-Markov process. Sci. Math. Jpn. 77, 719–723 (2013). Online e-2013

    MathSciNet  Google Scholar 

  4. Abundo, M.: On the first-passage time of an integrated Gauss-Markov process. Sci. Math. Jpn. 28, 1–14 (2015). Online e-2015

    Google Scholar 

  5. Abundo, M.: An inverse first-passage problem for one-dimensional diffusions with random starting point. Stat. Probab. Lett. 82(1), 7–14 (2012)

    Article  MathSciNet  Google Scholar 

  6. Abundo, M.: Some results about boundary crossing for Brownian motion. Ricerche di Matematica 50(2), 283–301 (2001)

    MathSciNet  MATH  Google Scholar 

  7. Elliot, R.J., Jeanblanc, M., Yor, M.: On models of default risk. Math. Finance 10, 179–196 (2000)

    Article  MathSciNet  Google Scholar 

  8. Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North-Holland Publishing Company, Amsterdam (1981)

    MATH  Google Scholar 

  9. Jeanblanc, M., Yor, M., Chesney, M.: Mathematical Methods for Financial Markets. Springer, London (2009). https://doi.org/10.1007/978-1-84628-737-4

    Book  MATH  Google Scholar 

  10. Karatzas, I., Shreve, S.: Brownian Motion and Stochastic Calculus. Springer, New York (1998)

    Book  Google Scholar 

  11. Klebaner, F.C.: Introduction to Stochastic Calculus with Applications, 2nd edn. Imperial College Press, London (2005)

    Book  Google Scholar 

  12. Revuz, D., Yor, M.: Continous Martingales and Brownian Motion. Springer, Heidelberg (1991). https://doi.org/10.1007/978-3-662-06400-9

    Book  MATH  Google Scholar 

  13. Ross, S.M.: Introduction to Probability Models, 10th edn. Academic Press, Elsevier, Burlington (2010)

    MATH  Google Scholar 

  14. Salminen, P.: On the first hitting time and the last exit time for a Brownian motion to/from a moving boundary. Adv. Appl. Probab. 20(2), 411–426 (1988)

    Article  MathSciNet  Google Scholar 

  15. Schumpeter, J.A.: Business Cycles: A Theoretical Historical and Statistical Analysis of the Capitalist Process. McGraw-Hill, New York (1939)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tor Vergata University, Rome, Italy

    Mario Abundo & Maria Beatrice Scioscia Santoro

Authors
  1. Mario Abundo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maria Beatrice Scioscia Santoro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Abundo .

Editor information

Editors and Affiliations

  1. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Abundo, M., Scioscia Santoro, M.B. (2020). On the Successive Passage Times of Certain One-Dimensional Diffusions. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2019. EUROCAST 2019. Lecture Notes in Computer Science(), vol 12013. Springer, Cham. https://doi.org/10.1007/978-3-030-45093-9_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-45093-9_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-45092-2

  • Online ISBN: 978-3-030-45093-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation