Tag - Stochastic analysis

Hendrik Weber: Noise, differential equations and quantum fields

27th March, 2024

Stochastic Analysis is concerned with solving differential equations in the presence of highly irregular random noise terms. The field has evolved from the foundational works by Itô in the 1940s and its method are used today in numerous modelling contexts. In the first half of this talk I will present my personal take on some of this history and some of the key ideas used. In the second half, I will discuss exciting developments of the last 10 years that show how methods developed for stochastic differential equations allow to give a new perspective on the classical problem to rigorously construct quantum fields.

Marco Cirant: On the long time behaviour of equilibria in a Kuramoto Mean Field Game

20th February, 2024

In a recent work, R. Carmona, Q. Cormier and M. Soner proposed a mean field game based on the classical Kuramoto model, originally motivated by systems of chemical and biological oscillators. Such MFG model exhibits several stationary equilibria, and the question of their ability to capture long time limits of dynamic equilibria is largely open. I will discuss in the talk how to show that, up to translations, there are two possible stationary equilibria only - the incoherent and the synchronised one - provided that the interaction parameter is large enough. Finally, I will present some local stability properties of the synchronised equilibrium.

Francesco De Vecchi: Non-commutative Lp-spaces and Grassmann stochastic analysis

12th June, 2023

We introduce a theory of non-commutative Lp spaces suitable for non-commutative probability in a non-tracial setting and use it to develop stochastic analysis of Grassmann-valued processes, including martingale inequalities, stochastic integrals with respect to Grassmann Itô processes, Girsanov’s formula and a weak formulation of Grassmann SDEs. We apply this new setting to the construction of several unbounded random variables, including a Grassmann analog of the φ24 Euclidean QFT in a bounded region.