Lounis, Amel2026-01-132026-01-132025https://dspace.ummto.dz/handle/ummto/29524This thesis focuses on the fractional Brownian motion (fBM), a stochastic process used to model long-memory phenomena using the Hurst parameter (H). It explores the mathematical properties of fBM, introduces methods to simulate its paths and estimate the H parameter, with applications in finance, hydrology, and biology.enParamètre de HurstProcessus gaussienMéthode de CholeskyMéthode de Wood et ChanMéthode de MandelbrotModélisation stochastique Applications en financehydrologieThesis