Sample paths of some Gaussian processes via Malliavin calculus

Thesis

In this thesis, we study the sample paths of some Gaussian processes using the methods from Malliavin calculus. To be more specific, we consider several interesting properties of fractional Brownian motion sample paths in the context of both probability measures and capacities. We are in particular interested in the non-differentiability, the modulus of continuity, the law of the iterated logarithm and self-avoiding properties. The capacities we use here are those induced by Brownian motions on the classical Wiener space, that is, we regard fractional Brownian motions with distinct Hurst parameters as a collection of Wiener functionals on the classical Wiener space and use the classical Wiener capacities as uniform measurements. We also formulate a capacity version of the large deviation principles for these functionals and determine the corresponding rate functions.

Authors: Li, J

• DOI: 10.5287/ora-x5grgokp1
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford