Stochastic differential equations driven by a fractional Brownian motion

Authors

  • Òscar Burés

Keywords:

fractional Brownian motion, stochastic differential equations, Malliavin calculus.

Abstract

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.

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How to Cite

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

Issue

Vol. 9 No. 1 (2024)

Section

Extended abstracts

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