A Generalized Ito's Formula in Two-Dimensions and Stochastic Lebesgue-Stieltjes Integrals
Chunrong Feng, Loughborough University
Huaizhong Zhao, Loughborough University
Abstract
In this
paper, a generalized Ito's formula for continuous functions of two-dimensional continuous
semimartingales is proved. The formula uses the local time of each
coordinate process of the semimartingale, the left space first derivatives and the second
derivative
∇ 1- ∇ 2-f, and the stochastic Lebesgue-Stieltjes integrals of two parameters.
The second
derivative ∇ 1- ∇ 2-f
is only assumed to be of locally bounded variation
in certain variables.
Integration by parts formulae are asserted for the
integrals of local times.
The two-parameter integral is defined as a natural
generalization of both the Ito
integral and the Lebesgue-Stieltjes integral through a type
of Ito isometry formula
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona. You can even send a scanned jpeg or pdf of this copyright form to the managing editor ejpecpme@math.univ-nantes.fr. as an attached file.
If a paper has several authors, the corresponding author signs the copyright form on behalf of all the authors.