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.

• 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.

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)