The existence and best L2-bounds for the Wiener type integrals , where X ranges through a wide class of Bessel-like centered processes, and f belongs to L2([0,1]), are discussed in terms of Fourier transforms associated with some characteristics of X, thus providing some unification of previous...

Wolfe (Stochastic Process. Appl. 12(3) (1982) 301) and Sato (Probab. Theory Related Fields 89(3) (1991) 285) gave two different representations of a random variable X1 with a self-decomposable distribution in terms of processes with independent increments. This paper shows how either of these...

We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere Sn−1⊂Rn and we obtain a Central Limit Theorem for a sequence of such Brownian motions. We also generalize the results to the case of the n-dimensional Ornstein–Uhlenbeck processes.