2009/12/16 by Jean Picard, Picard, Jean
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Fractional Differential Equations Solutions #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.0912.3168
to appear in "Séminaire de Probabilités"
openalex publication_date 2009/12/16 · arxiv created 2010/05/28 · arxiv updated 2010/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss the relationships between some classical representations of the fractional Brownian motion, as a stochastic integral with respect to a standard Brownian motion, or as a series of functions with independent Gaussian coefficients. The basic notions of fractional calculus which are needed for the study are introduced. As an application, we also prove some properties of the Cameron-Martin space of the fractional Brownian motion, and compare its law with the law of some of its variants. Several of the results which are given here are not new; our aim is to provide a unified treatment of some previous literature, and to give alternative proofs and additional results; we also try to be as self-contained as possible.