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ISS Informal Systems Seminar

An introduction to differential equations driven by rough path


Nov 24, 2023   10:00 AM — 11:00 AM

Torstein Nilssen Institute of Mathematics , University of Agder, Norway

Torstein Nilssen

Seminar in hybrid format at McGill University room MC 437 or 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 organizer
Aditya Mahajan organizer
Shuang Gao organizer
Borna Sayedana organizer
Alex Dunyak organizer


Room MC 437
McConnell Building
McGill University
3480, rue University
Montréal QC H3A 0E9

Associated organization

Centre for intelligent machines (CIM)

Research Axis

Research application