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Séminaire informel de théorie des systèmes (ISS)

An introduction to differential equations driven by rough path


24 nov. 2023   10h00 — 11h00

Torstein Nilssen Institute of Mathematics, University of Agder, Norvège

Torstein Nilssen

Séminaire en format hybride à l'Université McGill local MC 437 ou Zoom.

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.

Peter E. Caines responsable
Aditya Mahajan responsable
Shuang Gao responsable
Borna Sayedana responsable
Alex Dunyak responsable


Salle MC 437
Pavillon McConnell
Université McGill
3480, rue University
Montréal QC H3A 0E9

Organisme associé

Centre for intelligent machines (CIM)

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Application de recherche