Besov regularity of stochastic integrals with respect to the fractional Brownian motion with parameter \(H>1/2\) (Q1397969)

The authors consider the indefinite divergence integral \( X_t := \int_0^t u_s dB_s\), where \(\{B_t\), \(t \in [0,1] \}\) is a fractional Brownian motion with Hurst parameter \(H > 1/2\). The construction of the integral is based on Malliavin calculus and the authors study the Besov regularity of \( X_t\). They provide basic facts on Besov spaces and norms, Malliavin calculus and stochastic integrals with respect to fractional Brownian motion. The results present conditions on the integrand \(u\) such that the trajectories of \( X_t\) belong almost surely to certain Besov spaces.