Abstract
The purpose of the theory of stochastic integration is to give a reasonable meaning to the idea of a differential to as wide a class of stochastic processes as possible. We saw in Sect. 8 of Chap. I that using Stieltjes integration on a path-by-path basis excludes such fundamental processes as Brownian motion, and martingales in general. Markov processes also in general have paths of unbounded variation and are similarly excluded. Therefore we must find an approach more general than Stieltjes integration.
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
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Protter, P.E. (2005). Semimartingales and Stochastic Integrals. In: Stochastic Integration and Differential Equations. Stochastic Modelling and Applied Probability, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10061-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-662-10061-5_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05560-7
Online ISBN: 978-3-662-10061-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)