Théorèmes limites pour certaines fonctionnelles associées aux processus stables dans une classe d'espaces de besov

Limit Theorems for a Class of Additive Functionals of Symmetric Stable Process and Fractional Brownian Motion in Besov-Orlicz Spaces

“…This regularity is similar to that given in Ouahra and Eddahbi (2001) for fractional derivatives of local time of α-SSP and in Ouahra and Ouali (2009) for fBm case.…”

“…All these results are established in the space of continuous functions. Ouahra and Eddahbi (2001) extended the results of Fitzsimmons and Getoor (1992) to Holder spaces and Ouahra et al (2002) in Besov spaces and recently, Ouahra et al (2011) in Besov-Orlicz spaces. The result of Shieh (1996) was extended by Ouahra and Ouali (2009) in Besov spaces.…”

“…for any bounded or nonnegative Borel function f. Moreover, in Marcus and Rosen (1992) and in Ait Ouahra and Eddahbi (2001), for each T > 0 fixed, there .…”

Limit theorems and strong approximation for occupation times problem of sub-fractional Brownian motion in a class of Besov spaces

“…; .t// .t # 0/º:It is known from Ciesielski, Kerkyacharian and Roynette [7] that the subspace BFor the proof of our results, we need the following tightness and Kolmogorov criteria in the subspace B ! ; ;0 p;1 , proved by Ait Ouahra, Boufoussi and Lakhel[1] and Boufoussi, Lakhel and Dozzi[6].…”

Tightness in Besov–Orlicz spaces: Characterizations and applications

“…This characterization allowed to obtain in this spaces a tightness criterion and some regularities theorems of random trajectories (see for examples [1][2][3]). …”