AN EXTENSION OF THE LEVY CHARACTERIZATION TO FRACTIONAL BROWNIAN MOTION

作者：Mishura Yuliya^*; Valkeila Esko

来源：Annals of Probability, 2011, 39(2): 439-470.

DOI：10.1214/10-AOP555

• Fractional Brownian motion
• Levy theorem

Assume that X is a continuous square integrable process with zero mean, defined on some probability space (Omega, F, P). The classical characterization due to P. Levy says that X is a Brownian motion if and only if X and X(t)(2) - t, t >= 0, are martingales with respect to the intrinsic filtration F(X). We extend this result to fractional Brownian motion.

• 出版日期2011-3