Stochastic differential equations driven by a fractional Brownian motion

Autors/ores

  • Òscar Burés

Paraules clau:

fractional Brownian motion, stochastic differential equations, Malliavin calculus.

Resum

En aquest treball s’estudien les equacions diferencials estocàstiques (EDEs) dirigides per un moviment brownià fraccionari (fBm) amb paràmetre de Hurst H > 1/2. Es defineix la integral estocàstica respecte al fBm i es demostra l’existència i unicitat de solucions. També s’introdueix el càlcul de Malliavin en el context del fBm, i es prova que, amb condicions més fortes en els coeficients, la llei de la solució és absolutament contínua. Finalment, es donen fites d’estil gaussià per la densitat d’una família d’EDEs.

Descàrregues

Les dades de descàrrega encara no estan disponibles.

Descàrregues

Com citar

Burés, Òscar. (2024). Stochastic differential equations driven by a fractional Brownian motion. Reports@SCM, 9(1), 91–92. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154345

Número

Vol. 9 Núm. 1 (2024)

Secció

Extended abstracts

Llicència

The intellectual property of articles belongs to the respective authors.
On submitting articles for publication to the journal Reports@SCM, authors accept the following terms:
  1. Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Reports@SCM.
  2. Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.
  3. Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.
  4. Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.
  5. The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.
  6. The journal Reports@SCM is not responsible for the ideas and opinions expressed by the authors of the published articles.