Elements of Non-causal Calculus

  • Chapter
  • First Online:
Stochastic Calculus via Regularizations

Part of the book series: Bocconi & Springer Series ((BS,volume 11))

  • 798 Accesses

Abstract

We recall the stochastic calculus for anticipating integrands based on the very fruitful enlargement of filtrations technique. In this chapter we present some connections of that theory with the stochastic calculus via regularizations via the expression of substitution formulae.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. R. Coviello, F. Russo, Modeling financial assets without semimartingales. Preprint BiBoS 2006-06-219 (2006)

    Google Scholar 

  2. G. Di Nunno, B. Øksendal, F. Proske, Malliavin Calculus for Lévy Processes with Applications to Finance. Universitext (Springer, Berlin, 2009)

    Book  Google Scholar 

  3. T. Jeulin, Semi-martingales et grossissement d’une filtration, vol. 833. Lecture Notes in Mathematics (Springer, Berlin, 1980)

    Google Scholar 

  4. T. Jeulin, M. Yor, Inégalité de Hardy, semimartingales, et faux-amis, in Séminaire de Probabilités, XIII (University of Strasbourg, Strasbourg, 1977/78), vol. 721. Lecture Notes in Mathematics (Springer, Berlin, 1979), pp. 332–359

    Google Scholar 

  5. T. Jeulin, M. Yor (eds.), Grossissements de filtrations: exemples et applications, vol. 1118. Lecture Notes in Mathematics (Springer, Berlin, 1985). Papers from the seminar on stochastic calculus held at the Université de Paris VI, Paris, 1982/1983

    Google Scholar 

  6. R. Mansuy, M. Yor, Random Times and Enlargements of Filtrations in a Brownian Setting, vol. 1873. Lecture Notes in Mathematics (Springer, Berlin, 2006)

    Google Scholar 

  7. P.-A. Meyer, Sur un théorème de J. Jacod, in Séminaire de Probabilités, XII (Univ. Strasbourg, Strasbourg, 1976/1977), vol. 649. Lecture Notes in Mathematics (Springer, Berlin, 1978), pp. 57–60

    Google Scholar 

  8. E. Perkins, Stochastic integrals and progressive measurability—an example, in Seminar on Probability, XVII, vol. 986. Lecture Notes in Mathematics (Springer, Berlin, 1983), pp. 67–71

    Google Scholar 

  9. F. Russo, P. Vallois, Forward, backward and symmetric stochastic integration. Probab. Theory Related Fields 97(3), 403–421 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. F. Russo, P. Vallois, The generalized covariation process and Itô formula. Stochastic Process. Appl. 59(1), 81–104 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. F. Russo, P. Vallois, Stochastic calculus with respect to continuous finite quadratic variation processes. Stochastics Stochastics Rep. 70(1–2), 1–40 (2000)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Russo, F., Vallois, P. (2022). Elements of Non-causal Calculus. In: Stochastic Calculus via Regularizations. Bocconi & Springer Series, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-031-09446-0_11

Download citation

Publish with us

Policies and ethics

Navigation