MATS3500 Malliavin Calculus meets Stein鈥檚 method (3 op)
Arvosteluasteikko
贬测惫盲办蝉测迟迟测-丑测濒盲迟迟测
Opetuskieli/-kielet
englanti
痴补蝉迟耻耻丑别苍办颈濒枚(迟)
Stefan Geiss
Osaamistavoitteet
- Student has basic knowledge of Malliavin calculus and Stein鈥檚 method
- Student understands the use of combination of Malliavin calculus and Stein's method to prove central limit theorems
Suoritustavat
Lecture and written assignment
厂颈蝉盲濒迟枚
- Preliminaries: Gaussian Random Vectors, Hermite Polynomials, Gaussian Processes.
- Fractional Brownian Motion.
- Malliavin Calculus in a Nutshell
- Stein鈥檚 Lemma
- Combining Stein鈥檚 Method with Malliavin Calculus
- Central Limit Theorems for Fractional Brownian motion
Kirjallisuus
| ISBN-numero | Tekij盲, julkaisuvuosi, teoksen nimi, julkaisija |
|---|---|
| 978-88-470-2823-4 | Nourdin (2012): Selected aspects of fractional Brownian motion. Bocconi & Springer Series, 4. Springer, Milan; Bocconi University Press, Milan. |
| 9781107017771 | Nourdin, Peccati (2012): Normal approximations with Malliavin calculus: From Stein鈥檚 method to universality. Cambridge Tracts in Mathematics, 192. Cambridge University Press, Cambridge. |
| 978-3-540-28329-4 | Nualart (2006): The Malliavin calculus and related topics (Probability and Its Applications). Second edition. Springer. |
Arviointiperusteet
Student does an assignment, returns it to teacher and teacher evaluates whether pass or not.
Esitietovaatimukset
Basic background in Probability