Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

On Thursday, January 7, and Friday, January 8, 1999, MaPhySto will,
as part of a thematic period on *Lévy 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
Lévy Processes: Theory and Applications, January 18-22, 1999.

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

- Professor Richard Dudley (MIT),
- Dr. Rimas Norvaisa (Institute of Mathematics and Cybernetics, Vilnius).

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.

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]

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.

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

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`.