Limit theorems for Gaussian fields via Chaos Expansions and Applications
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916299722981376 |
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| author | Giorgio, Giacomo |
| author_facet | Giorgio, Giacomo |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15801 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit theorems for Gaussian fields via Chaos Expansions and Applications Giorgio, Giacomo Probability 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). |
| title | Limit theorems for Gaussian fields via Chaos Expansions and Applications |
| topic | Probability |
| url | https://arxiv.org/abs/2406.15801 |