Selected Aspects of Fractional Brownian Motion

Ivan Nourdin is full professor in Mathematics at Université de Lorraine (France). His research interests include Malliavin calculus, Stein's method and free probability.

From the reviews:“This short monograph by Ivan Nourdin deals with several aspects of fractional Brownian motion (fBm) ranging from basic properties over integration theory to non-commutative fractional Brownian motion. … The text is well written and almost all results are given with complete proofs. It is certainly a valuable contribution to the literature on fBm and will be a helpful source for everybody interested in new developments on fBm and its relation to other fields.” (Hilmar Mai, zbMATH, Vol. 1274, 2013)

• 1. Preliminaries.- 2. Fractional Brownian motion.- 3. Integration with respect to fractional Brownian motion.- 4. Supremum of the fractional Brownian motion.- 5. Malliavin calculus in a nutshell.- 6. Central limit theorem on the Wiener space.- 7. Weak convergence of partial sums of stationary sequences.- 8. Non-commutative fractional Brownian motion.