Abstract
In this chapter, we use the quasi-surely analysis theory to develop Itô’s integrals without the quasi-continuity condition. This allows us to define Itô’s integral on stopping time interval. In particular, this new formulation can be applied to obtain Itô’s formula for a general \(C^{1,2}\)-function, thus extending previously available results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer-Verlag GmbH Germany, part of Springer Nature
About this chapter
Cite this chapter
Peng, S. (2019). Some Further Results of Itô’s Calculus. In: Nonlinear Expectations and Stochastic Calculus under Uncertainty. Probability Theory and Stochastic Modelling, vol 95. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59903-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-662-59903-7_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-59902-0
Online ISBN: 978-3-662-59903-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)