Relations between harnesses and initial enlargements of the filtration of a Lévy process with its positions at fixed times are investigated.

A general methodology allowing to solve the Skorokhod stopping problem for positive functionals of Brownian excursions, with the help of Brownian local time, is developed. The stopping times we consider have the following form: T[mu]=inf{t0: Ft[greater-or-equal, slanted][phi][mu]F(Lt)}. As an...

We discuss Brownian analogues of a celebrated theorem, due to Burke, which states that the output of a (stable, stationary) M/M/1 queue is Poisson, and the related notion of quasireversibility. A direct analogue of Burke's theorem for the Brownian queue was stated and proved by Harrison...

We study absolute-continuity relationships for a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of such processes are locally equivalent to the law of the original process and we compute...

Motivated by the Kyle-Back model of "insider trading", we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition, i.e., their Doob-Meyer decomposition as semimartingales in their own filtration. In particular we characterize...

Motivated by asymptotic problems in the theory of empirical processes, and specifically by tests of independence, we study the law of quadratic functionals of the (weighted) Brownian sheet and of the bivariate Brownian bridge on [0,1]2. In particular: (i) we use Fubini-type techniques to...

As discussed in Madan and Yor (2002) [10], under certain conditions on a family (Hr,r0) of Hardy–Littlewood functions, Markovian Martingales (BTHr) may be constructed. We take advantage of the explicit character of the Azéma–Yor (Skorokhod embedding) algorithm, to describe precisely some...