For a bivariate Lévy process ([xi]t,[eta]t)t=0 the generalised Ornstein-Uhlenbeck (GOU) process is defined as where . We present conditions on the characteristic triplet of ([xi],[eta]) which ensure certain ruin for the GOU. We present a detailed analysis on the structure of the upper and lower...

Protein translocation in cells has been modelled by Brownian ratchets. In such models, the protein diffuses through a nanopore. On one side of the pore, ratcheting molecules bind to the protein and hinder it to diffuse out of the pore. We study a Brownian ratchet by means of a reflected Brownian...

We prove the convergence in law, in the space of continuous functions , of the Russo-Vallois symmetric integral of a non-adapted process with respect to the fractional Brownian motion with Hurst parameter H1/2 to the Russo-Vallois symmetric integral with respect to the fractional Brownian motion...

Let Sn be a centered random walk with a finite variance, and consider the sequence , which we call an integrated random walk. We are interested in the asymptotics of as N--[infinity]. Sinai (1992) [15] proved that pN[asymptotically equal to]N-1/4 if Sn is a simple random walk. We show that...

We address a rate control problem associated with a single server Markovian queueing system with customer abandonment in heavy traffic. The controller can choose a buffer size for the queueing system and also can dynamically control the service rate (equivalently the arrival rate) depending on...

The asymptotic behavior of a stochastic network represented by a birth and death processes of particles on a compact state space is analyzed. In the births, particles are created at rate [lambda]+ and their location is independent of the current configuration. Deaths are due to negative...

We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. The rates are computed explicitly. We show that the rates are very similar to those of an i.i.d....

We consider the linear stochastic wave equation with spatially homogeneous Gaussian noise, which is fractional in time with index H1/2. We show that the necessary and sufficient condition for the existence of the solution is a relaxation of the condition obtained in Dalang (1999) [10], where the...

Among Professor Kiyosi Itô's achievements, there is the Itô-Nisio theorem, a completely general theorem relative to the Fourier series decomposition of Brownian motion. In this paper, some of its applications will be reviewed, and new applications to 1-soliton solutions to the Korteweg-de...

Cramér's theorem provides an estimate for the tail probability of the maximum of a random walk with negative drift and increments having a moment generating function finite in a neighborhood of the origin. The class of (g,F)-processes generalizes in a natural way random walks and fractional...