We consider a Poisson process [eta] on a measurable space equipped with a strict partial ordering, assumed to be total almost everywhere with respect to the intensity measure [lambda] of [eta]. We give a Clark-Ocone type formula providing an explicit representation of square integrable...

Under the framework of G-expectation and G-Brownian motion, we introduce Itô's integral for stochastic processes without assuming quasi-continuity. Then we can obtain Itô's integral on stopping time interval. This new formulation permits us to obtain Itô's formula for a general C1,2-function,...

We consider the heavy-traffic approximation to the GI/M/s queueing system in the Halfin-Whitt regime, where both the number of servers s and the arrival rate [lambda] grow large (taking the service rate as unity), with and [beta] some constant. In this asymptotic regime, the queue length process...

We define and solve Volterra equations driven by a non-differentiable signal, by means of a variant of the rough paths theory which allows us to handle generalized integrals weighted by an exponential coefficient. The results are applied to a standard rough path , with [gamma]1/3, which includes...

For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of subnormal or normal deviations from the origin; in...

For a given filtered probability space , an -adapted continuous increasing process [Lambda] and a positive - local martingale N such that [Lambda]0=0 and Nte-[Lambda]t=1, we construct a probability measure and a random time [tau] such that and . The probability is linked with the well-known Cox...

This article introduces and analyzes multilevel Monte Carlo schemes for the evaluation of the expectation , where Y=(Yt)t[set membership, variant][0,1] is a solution of a stochastic differential equation driven by a Lévy process. Upper bounds are provided for the worst case error over the class...

A real harmonizable multifractional stable process is defined, its Hölder continuity and localizability are proved. The existence of local time is shown and its regularity is established.

The motion of a finite number of point vortices on a two-dimensional periodic domain is considered. In the deterministic case it is known to be well posed only for almost every initial configuration. Coalescence of vortices may occur for certain initial conditions. We prove that when ageneric...

We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers according to a spectrally positive Lévy process Y(t) which is reflected at 0. When the exponential clock ends, the additional state-dependent service requirement modifies the workload so that...