Abstract
This article investigates filtrations created by the increments-processes of processes with independent increments: Suppose two processes create the same filtrations, when will the processes of their increments also create the same filtrations?
Our main result is that the processes of increments of two extremal continuous martingales with independent increments create the same filtrations if and only if either process admits a deterministic representation with respect to the other.
Keywords
- Brownian Motion
- Polish Group
- Standard Brownian Motion
- Independent Increment
- Stationary Increment
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin/Heidelberg
About this chapter
Cite this chapter
Bühler, H. (2005). Information-equivalence: On Filtrations Created by Independent Increments. In: Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVIII. Lecture Notes in Mathematics, vol 1857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31449-3_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-31449-3_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23973-4
Online ISBN: 978-3-540-31449-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
