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Event

An introduction to differential equations driven by rough path

Friday, November 24, 2023 10:00to11:00
McConnell Engineering Building Zames Seminar Room, MC 437, 3480 rue University, Montreal, QC, H3A 0E9, CA

Informal Systems Seminar (ISS) Centre for Intelligent Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisions (GERAD)

Speaker: Torstein Nilssen

*Note that this is a hybrid event*


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Abstract: In this talk I will start from a differential equation and show that the deterministic integration theory of Young (1936) is not suitable to give a pathwise description of stochastic differential equations. I will then present the insight by Terry Lyons (1998) that the missing ingredient is the iterated integral of the Brownian motion as well as a Taylor expansion type equation which gives intuition into why this is the correct object. We will then consider the ansatz of controlled paths and how it can be used to set up a fixed point mapping for rough differential equations. If time allows we will look at applications of the theory to Wong-Zakai approximations and fractional Brownian motion.

Affiliation : Torstein Kastberg is an Associate Professor at Institue of Mathematics at University of Agder, Norway.

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