Prof  Markus Riedle

Title: Cylindrical Lévy Processes and Stochastic Integration

Abstract

Cylindrical Lévy processes are generalised processes in Banach or Hilbert spaces that do not take values in the underlying space. Prominent examples include the cylindrical Brownian motion and the standard symmetric α-stable cylindrical process. While these processes are natural extensions of their finite-dimensional counterparts, they cannot be realised as classical stochastic processes attaining values in the underlying space.

In this talk, we introduce the concept of cylindrical Lévy processes and explore some key examples. The main focus is on developing a theory for stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces. This approach builds on a method by Kwapień and Woyczyński, employing a decoupling inequality. The largest admissible space of integrands is identified as the space of predictable processes taking values in a modular space, determined by the cylindrical semimartingale characteristics of the driving noise.

 This talk is based on joint works with G. Bodó, A. Jakubowski, T. Kosmala and others.

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