Skip to main content
SpringerLink
Log in

Two-sided stochastic calculus for spdes

  • Conference paper
  • First Online:
Book cover Stochastic Partial Differential Equations and Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1236))

Abstract

In [9], a stochastic calculus was developped for functions of both a forward and a backward finite dimensional diffusion processes, which requires the definition of a certain class of stochastic integrals with anticipating integrands. The aim of this paper is to show how these results can be adapted to the case of a pair of linear parabolic SPDEs.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. N. Krylov, B. Rosovskii: On the first integral and Liouville equations for diffusion processes in Stochastic Differential Systems M. Arato, D. Vermes, A. Balakrishnan eds, Lecture notes in Control and Info. Sciences 36, Springer-Verlag (1981)

    Google Scholar 

  2. M. Métivier, J. Pellaumail: Stochastic Integration Acad. Press (1980)

    Google Scholar 

  3. D. Nualart, E. Pardoux: Non adapted stochastic calculus, to appear

    Google Scholar 

  4. D. Nualart, M. Zakai: Generalized stochastic integrals and the Malliavin calculus, Preprint.

    Google Scholar 

  5. D. Ocone: Probability distributions of solutions to some stochastic partial differential equations, these Proceedings.

    Google Scholar 

  6. E. Pardoux Stochastic PDEs and filtering of diffusion processes, Stochastics 3, 127–167 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  7. E. Pardoux Equations du filtrage nonlinéaire, de la prédiction et du lissage, Stochastics 6, 193–231 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  8. E. Pardoux: Equations du lissage nonlinéaire, in Filtering and Control of Random Processes, H. Korezlioglu, G. Mazziotto, J. Szpirglas eds, Lecture Notes in Control and Info. Sciences 61 (1984)

    Google Scholar 

  9. E. Pardoux, P. Protter A two-sided stochastic integral and its calculus, Preprint.

    Google Scholar 

  10. A. Skorohod On a generalization of a stochastic integral, Theory of Prob. and Appl. 20, 219–233 (1975)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathématiques — Case H, Université de Provence, F13331, Marseille Cedex 3 and INRIA-Sophia-Antipolis

    E. Pardoux

  2. INRIA-Sophia-Antipolis, France

    E. Pardoux

Authors
  1. E. Pardoux
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Giuseppe Da Prato Luciano Tubaro

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Pardoux, E. (1987). Two-sided stochastic calculus for spdes. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications. Lecture Notes in Mathematics, vol 1236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072891

Download citation

  • DOI: https://doi.org/10.1007/BFb0072891

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17211-6

  • Online ISBN: 978-3-540-47408-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation