57
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On the asymptotic behavior of an approximation of SIEs driven by p‐semimartingales

Pages 103-116 | Received 31 Oct 2001, Published online: 14 Oct 2010

References

  • Bouleau , N. and Lépingle , D. 1994 . Numerical Methods for Stochastic Processes , New York : Wiley .
  • Dudley , R.M. 1999 . Picard iteration and p‐variation: the work of Lyons (1994) . Mini‐proceedings: Workshop on Product Integrals and Pathwise Integration . 1999 , MaPhySto, Aarhus.
  • Dudley , R.M. and Norvaiša , R. 1998 . An Introduction to p‐variation and Young Integrals , Aarhus University . Lecture Notes No.1
  • Dudley , R.M. and Norvaiša , R. 1999 . Product Integrals, Young integrals and p‐variation , volume 1703 , Springer . Lecture Notes Math.
  • Duncan , T.E. , Hu , Y. and Pasik‐Duncan , B. 2000 . Stochastic calculus for fractional Brownian motion . I.Theory. SIAMJ.Control Optim. , 38 : 582 – 612 .
  • Hofmann , N. , Müller‐Gronbach , T. and Ritter , K. 2000 . Step‐size control for the uniform approximation of systems of stochastic differential equations with additive noise . Ann. Appl. Probab. , 10 (2) : 616 – 633 .
  • Kubilius , K. “ The existence and uniqueness of the solution of the integral equation driven by a p‐semimartingale of the special type ” . In Stochastic Processes Appl (to appear 2002)
  • Kubilius , K. 1999 . An approximation of a non‐linear integral equation driven by a function of bounded p‐variation . Lith. Math. J. , 39 (3) : 317 – 330 .
  • Norvaiša , R. 2000 . Quadratic variation, p‐variation and integration with applications to stock price modeling Unpublished manuscript
  • Young , L.C. 1936 . An inequality of the Hölder type, connected with Stieltjes integration . Acta Math. , 67 : 251 – 282 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.