The Department of Mathematical Sciences will host Dr. Sonja Cox from the Korteweg-de Vries Institute for Mathematics, University of Amsterdam, on Friday, October 20, 2023, from 11:20 a.m. – 12:20 p.m., as part of its math seminar series. Dr. Cox will present, “Infinite-dimensional Wishart processes.” This free event will take place in BSB, Room 132. 



A Wishart process is a stochastic process $(X_t)_{t\geq 0}$ taking values in the space of positive semi-definite matrices such that $X_t$ has a (generalized) Wishart distribution for every $t\geq 0$. Wishart processes were introduced in the ’90s by Bru and have become a popular choice for modeling stochastic covariance. For example, Wishart processes are used in multi-dimensional Heston models to describe the instantaneous volatility of multiple assets. Models for energy and interest rate markets involve stochastic \emph{partial} differential equations, and thus call for infinite-dimensional covariance models. In our work, we introduce and analyze infinite-dimensional Wishart processes, and discuss some of their advantages and shortcomings.