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MaPhySto
Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

Concentrated Advanced Course on

Product Integrals and Pathwise Integration

Lectures by R. Dudley and R. Norvaisa

January 7-8, 1999

Auditorium G1

Department of Mathematical Sciences

University of Aarhus

Background

On Thursday, January 7, and Friday, January 8, 1999, MaPhySto will, as part of a thematic period on LÚvy Processes, Product Integrals and Pathwise Integration in January 1999 organize the above-mentioned Concentrated Advanced Course. The thematic period also comprises a Workshop on Pathwise Integration and Product Integrals, January 11-13, 1999, and a Conference on LÚvy Processes: Theory and Applications, January 18-22, 1999.

Format

Two leading experts have agreed to be principal lecturers for the Advanced Course:

They recently finished a volume of Lecture Notes on the topic. The Course addresses PhD students, postdocs and researchers who want to learn about the history and recent developments in the classical approach to integration.

The Course focuses on the Riemann-Stieltjes integral and several of its extensions when neither integrator nor integrand have bounded variation. These integrals, as well as the product integral will be discussed with a view towards applications to sample functions of stochastic processes.

Schedule

Thursday
9.30-10.30 R. Dudley: How should integrals of Stieltjes type be defined?
10.50-11.50 R. Norvaisa: Stochastic integrals
12.00-12.30 R. Dudley: Lyons' work on obstacles to pathwise Ito integration
12.30-13.30 lunch (free for registered participants)
13.30-14.15 R. Dudley: Differentiability with respect to p-variation norms (I)
14.20-15.05 R. Dudley: Differentiability with respect to p-variation norms (II)
15.20-16.05 R. Norvaisa: Properties of p-variation (I)
16.15-17.00 R. Norvaisa: Properties of p-variation (II)
Friday
9.30-10.30 R. Norvaisa: Stochastic processes and p-variation
10.45-11.45 R. Dudley: Empirical processes and p-variation
12.00-13.00 lunch (free for registered participants)
13.00-14.00 R. Norvaisa: Integration
14.10-14.40 R. Dudley: Ordinary differential equations and product integrals
15.00-16.00 R. Norvaisa: Product integrals
16.10-16.40 R. Dudley: Other aspects of product integrals

The latter item is the main objective of the Workshop that takes place in the week following the Advanced Course. It is intended to bring together specialists from different areas such as probability theory, stochastic processes, statistics, physics, finance and analysis, and to discuss pathwise, stochastic and product integration techniques.

It is the main goal of the organisers and the principal lecturers to achieve a fruitful, perhaps controversial, discussion about pathwise integration techniques, their advantages and limits.

The notes for the course are now available (in zipped postscript format):
[complete] [Chapters 1 and 2 | Chapters 3 and 4 | Chapters 5 and 6 | Chapter 7 and References]

Support

No financial support is available. Participants are expected to have their expenses covered by their home institutions. Note however, that there is no registration fee.

Registration

The deadline for registration was December 1, 1998. Late registrations may be considered.

More Information

Please make any further inquiries to MaPhySto (maphysto@mi.aau.dk.)


This document, http://www.maphysto.dk/oldpages/events/LevyProc/CAC/index.html, was last modified January 19, 2004. Questions or comments to the contents of this document should be directed to maphysto@maphysto.dk.