Mini-Workshop of the ANR STARS

Martingale Theoretic Approach to Noncommutative Stochastic Calculus

28 juin 2023, 09:30

1h

salle Huron (1R1 - 106) (IMT)

Orateur

Vaki Nikitopoulos

Description

Free -- or more generally noncommutative -- stochastic analysis is often useful for describing the large $N$-limit of an ensemble $X^{(N)}=(X_t^{(N)}{)}_{t\ge 0}$ of $N\times N$ matrix stochastic processes. We describe a flexible general theory of noncommutative stochastic calculus that is useful for describing the large-$N$ limits of solutions to $N\times N$ matrix stochastic differential equations. Our theory generalizes the theories of Biane-Speicher for free Brownian motion and Donati-Martin for $q$-Brownian motion. Moreover, it unifies these theories with some aspects of the classical theory of stochastic calculus. This is joint work with D. Jekel and T. Kemp.