Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
On the Itô–Wentzell formula for distribution-valued processes and related topics
Download PDF
Download PDF
  • Published: 11 March 2010

On the Itô–Wentzell formula for distribution-valued processes and related topics

  • N. V. Krylov1 

Probability Theory and Related Fields volume 150, pages 295–319 (2011)Cite this article

  • 404 Accesses

  • 45 Citations

  • Metrics details

Abstract

We prove the Itô–Wentzell formula for processes with values in the space of generalized functions by using the stochastic Fubini theorem and the Itô–Wentzell formula for real-valued processes, appropriate versions of which are also proved.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Adams R.A.: Sobolev Spaces. Academic Press, New York (1975)

    MATH  Google Scholar 

  2. Kallianpur G., Striebel C.: Stochastic differential equations occurring in the estimation of continuous parameter stochastic processes. Teor. Verojatnost. i Primenen. 14, 597–622 (1969)

    MathSciNet  MATH  Google Scholar 

  3. Krylov N.V.: On SPDEs and superdiffusions. Ann. Probab. 25(4), 1789–1809 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Krylov, N.V.: An analytic approach to SPDEs. In: Stochastic Partial Differential Equations: Six Perspectives, Mathematical Surveys and Monographs, vol. 64, pp. 185–242. AMS, Providence (1999)

  5. Kunita, H.: Stochastic flows and stochastic differential equations. In: Cambridge Studies in Advanced Mathematics, vol. 24. Cambridge University Press, Cambridge (1997)

  6. Protter, P.E.: Stochastic integration and differential equations. In: Stochastic Modelling and Applied Probability, vol. 21, 2nd edn, Version 2.1, Corrected third printing. Springer, Berlin (2005)

  7. Rozovskii B.L.: Stochastic Evolution Systems. Kluwer, Dordrecht (1990)

    MATH  Google Scholar 

  8. van Neerven, J., Veraar, M.: On the stochastic Fubini theorem in infinite dimensions. In: Stochastic partial differential equations and applications-VII, Lecture Notes in Pure Applied Mathematics, vol. 245, pp. 323–336. Chapman & Hall/CRC, Boca Raton (2006)

Download references

Author information

Authors and Affiliations

  1. University of Minnesota, 127 Vincent Hall, Minneapolis, MN, 55455, USA

    N. V. Krylov

Authors
  1. N. V. Krylov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. V. Krylov.

Additional information

The work was partially supported by NSF grant DMS-0653121.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Krylov, N.V. On the Itô–Wentzell formula for distribution-valued processes and related topics. Probab. Theory Relat. Fields 150, 295–319 (2011). https://doi.org/10.1007/s00440-010-0275-x

Download citation

  • Received: 14 May 2009

  • Revised: 03 February 2010

  • Published: 11 March 2010

  • Issue Date: June 2011

  • DOI: https://doi.org/10.1007/s00440-010-0275-x

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Itô–Wentzell formula
  • Stochastic Fubini theorem

Mathematics Subject Classification (2000)

  • 60H05
  • 60H15
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature