My research focuses on cylindrical Lévy processes and their role as driving noises in infinite-dimensional stochastic systems. Together with D. Applebaum, I introduced the concept of cylindrical Lévy processes, which naturally generalise cylindrical Brownian motion—the standard model for random perturbations of complex dynamical systems.

I have developed a comprehensive integration theory in Hilbert and Banach spaces, providing a rigorous framework for stochastic evolution equations and SPDEs without imposing restrictive moment assumptions. This work establishes fundamental analytical tools, including regularisation techniques and structural properties of the resulting processes, and contributes to a unified understanding of Lévy-driven phenomena in infinite dimensions.

Slides from a short lecture course can be found [here].

For a first introduction to cylindrical Lévy processes, I recommend the following articles:

• Cylindrical Lévy processes in Banach spaces (with D. Applebaum),
  Proc. Lond. Math. Soc. 101 (2010), 697–726.

• Infinitely divisible cylindrical measures on Banach spaces,
  Studia Math. 207 (2011), 235–256.

• Ornstein–Uhlenbeck processes driven by cylindrical Lévy processes
  Potential Anal. 42 (2015), 809–838.

• Stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces  (with G. Bodó),
  J. Lond. Math. Soc. (2) 112 (2025), no. 3, Paper No. e70298, 42 pp.