Limit theorems for Gaussian fields via Chaos Expansions and Applications
| Autor: | Giorgio, Giacomo |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this PhD thesis, we apply a combination of Malliavin calculus and Stein's method in the framework of probability approximations. The specific problems we tackle with these methods are motivated by probabilistic models in cosmology (Part I: Quantitative CLTs for non linear functionals of random hyperspherical harmonics) and finance (Part II: The fractional Ornstein-Uhlenbeck process in rough volatility modelling). In this second part we also apply techniques from Large Deviations theory (Section: Short-time asymptotics for non self-similar stochastic volatility models). Comment: PhD thesis |
| Databáze: | arXiv |
| Externí odkaz: |
|