For a large class of ℝ+ valued, continuous local martingales (Mtt ≥ 0), with M0 = 1 and M∞ = 0, the put quantity: ΠM (K,t) = E ((K - Mt)+) turns out to be the distribution function in both variables K and t, for K ≤ 1 and t ≥ 0, of a probability γM on [0,1] × [0, ∞[. In this...

We prove that the law of the euclidean norm of an n-dimensional Brownian bridge is, in general, only equivalent and not equal to the law of a n-dimensional Bessel bridge and we compute explicitly the mutual density. Relations with Bessel processes with drifts are also discussed.

In previous papers [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered powers of Bessel processes, I, Markov Processes Related Fields (2006) (in press); T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered Bessel and related processes, II, Alea (2006) (in press)], the authors...

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...