Skip to main content
SpringerLink
Log in

The stochastic integral as a vector measure

  • Stochastic Analysis And Probability
  • Conference paper
  • First Online:
Measure Theory Oberwolfach 1979

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 794))

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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.

References

  1. BICHTELER, K. "Stochastic Integrators", Bull. A.M.S. 1/2, September 1979.

    Google Scholar 

  2. BICHTELER, K. "Stochastic integration and Lp-theory of semimartingales", (to appear).

    Google Scholar 

  3. BICHTELER, K. "Function norms and function metrics satisfying the dominated convergence theorem, and their applications", (to appear).

    Google Scholar 

  4. BICHTELER, K. "Integration theory", Lecture Notes Math #315, Springer, Berlin, 1973.

    MATH  Google Scholar 

  5. BICHTELER, K. "Measures with values in non-locally convex spaces", In Proc. Oberwolfach Conf. on Vector Measures, Lecture Notes Math. #541, Springer, 1976.

    Google Scholar 

  6. DELLACHERIE, C. Capacités et Processus Stochastiques, Springer, Berlin 1972.

    MATH  Google Scholar 

  7. DELLACHERIE, C. "Quelques applications du lemme de Borel-Cantelli à la théorie des semimartingales", Sém. Prob. XII, 742–745, Lecture Notes #649, Springer, Berlin 1978.

    Google Scholar 

  8. DOLEANS-DADE, C. "On the existence and unicity of solutions of a stochastic differential equation", Z. Wahrsch., 34(1976), 93–101.

    Google Scholar 

  9. DOLEANS-DADE, C. and MEYER, P.A. "Équations différentielles stochastiques", Séminaire de Probabilités XI, Lecture Notes in Math, #581, 376–382, Springer, Berlin 1977.

    Chapter  Google Scholar 

  10. EMERY, M. "Stabilité des solution des équations différentielles stochastiques; application aux intégrales multiplicatives stochastiques", Z. Wahrsch., 41(1978), 241–262.

    Article  MathSciNet  MATH  Google Scholar 

  11. EMERY, M. "Équations différentielles stochastiques: La méthode de Métivier et Pellaumail", Séminaire de Probabilités de Strasbourg XIV, (to appear).

    Google Scholar 

  12. HALMOS, P.R. Measure Theory, Van Nostrand, New York, 1950.

    Book  MATH  Google Scholar 

  13. ITÔ, K. "Stochastic integral", Proc. Imperial Acad. Tokyo, 20(1944), 519–524.

    Article  MATH  Google Scholar 

  14. JACOD, J. "Calcul stochastique et problèmes de martingales", Lect. Notes Math. #714, Springer, 1979.

    Google Scholar 

  15. KUSSMAUL,. "Stochastic integration and generalized martingales", Research Notes, Pittman, London, 1977.

    MATH  Google Scholar 

  16. MAUREY, B. "Theorèmes de factorization pour les operateurs linéaires a valeurs dans les espaces Lp", Astérisque, 11(1974), 1–163.

    MathSciNet  MATH  Google Scholar 

  17. METIVIER, M. "Reelle und vektorwertige Quasimartingale und die Theorie der stochastischen Integration", Lect. Notes Math. #607, Springer, Berlin 1977.

    MATH  Google Scholar 

  18. METIVIER, M. and PELLAUMAIL, J. "Mesure stochastique a valeur dans les espaces L0", Z. Wahrsch., 40/2 (1977).

    Google Scholar 

  19. METIVIER, M. and PELLAUMAIL, J. "Une formule de majoration pour martingales; et sur une équation stochastique assez générale", C.R. Acad. Sci. Paris, 285 and 921(197 ), 685.

    Google Scholar 

  20. MEYER, P.-A. "Un cours sur les intégrales stochastiques", Lect. Notes Math. #511, Springer 1976.

    Google Scholar 

  21. MEYER, P.-A. "Charactérisation des semimartingales d'après Dellacherie", Séminaire de Probabilités XIII, 620–623, Lect. Notes Math. #721, Springer, Berlin 1979.

    Chapter  Google Scholar 

  22. MEYER, P.-A. "Inégalités de normes pour les intégrales stochastiques", Séminaire de Probabilités XII, 757–762, Lect. Notes Math. #XII, Springer, Berlin 1978.

    Chapter  Google Scholar 

  23. PELLAUMAIL, J. "Sur l'intégrale stochastique et la décomposition de Doob-Meyre", Asterisque 9(1973), 1–124.

    MathSciNet  MATH  Google Scholar 

  24. PELLAUMAIL, J. "Une example d'intégrale d'une fonction réelle par rapport à une mesure vectorielle: l'intégrale stochastique", C.R. Acad. Sci. Paris, 274(1972), 1369–1372.

    MathSciNet  MATH  Google Scholar 

  25. PROTTER, P. "On the existence, uniqueness, convergence and explosions of solutions of systems of stochastic differential equations", Ann. Prob., 5(1977), 243–261.

    Article  MathSciNet  MATH  Google Scholar 

  26. PROTTER, P. "Right-continuous solutions of systems of stochastic integral equations", J. Multivariate Analysis, 7(1977), 204–214.

    Article  MathSciNet  MATH  Google Scholar 

  27. PROTTER, P. "Markov solutions of stochastic differential equations", Z. Wahrsch., 41(1977), 39–58.

    Article  MathSciNet  MATH  Google Scholar 

  28. PROTTER, P. "Hp-stability of solutions of stochastic differential equations", Z. Wahrsch., 44(1978), 337–352.

    Article  MathSciNet  MATH  Google Scholar 

  29. ROSENTHAL, H. "On subspaces of Lp", Ann. Math., 97(1973), #2, 344–373.

    Article  MATH  Google Scholar 

  30. THOMAS, E. "L'intégration par rapport à une mesure de Radon vectorielle", Ann. Inst. Fourier, 20(1970), 55–191.

    Article  MathSciNet  MATH  Google Scholar 

  31. YOR, M. "Inégalites entre processus minces et applications", Comptes Rendus Acad. Sci., 286(1978), #(A), 799–802.

    MATH  Google Scholar 

  32. YOR, M. "Quelques interactions entre mesures vectorielles et intégrales stochastiques", Lect. Notes Math. #713, Springer 1979.

    Google Scholar 

  33. YOR, M. "Remarques sur les normes Hp de (semi) martingales", C.R. Acad. Sci. Paris, 287(1978), 461–465.

    MathSciNet  MATH  Google Scholar 

  34. ZYGMUND, A. Trigonometric Series, Cambridge 1959.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, 78712, Austin, Texas, U.S.A.

    Klaus Bichteler

Authors
  1. Klaus Bichteler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Dietrich Kölzow

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Bichteler, K. (1980). The stochastic integral as a vector measure. In: Kölzow, D. (eds) Measure Theory Oberwolfach 1979. Lecture Notes in Mathematics, vol 794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088236

Download citation

  • DOI: https://doi.org/10.1007/BFb0088236

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09979-6

  • Online ISBN: 978-3-540-39221-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation