We consider a model for a polymer interacting with an attractive wall through a random sequence of charges. We focus on the so-called diluted limit, when the charges are very rare but have strong intensity. In this regime, we determine the quenched critical point of the model, showing that it is...

We consider an initial Eve-population and a population of neutral mutants, such that the total population dies out in finite time. We describe the evolution of the Eve-population and the total population with continuous state branching processes, and the neutral mutation procedure can be seen as...

We construct the Laplace approximation of the Lebesgue density for a discrete partial observation of a multi-dimensional stochastic differential equation. This approximation may be computed integrating systems of ordinary differential equations. The construction of the Laplace approximation...

Let X=(Xt)t=0 be a Lévy process with absolutely continuous Lévy measure [nu]. Small-time expansions of arbitrary polynomial order in t are obtained for the tails , y0, of the process, assuming smoothness conditions on the Lévy density away from the origin. By imposing additional regularity...

We consider branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If d=3 and the environment is "not too random", then, the total population grows as fast as its expectation with strictly...

For an arbitrary integer N=2, this paper gives the construction of a strictly stationary (and ergodic), N-tuplewise independent sequence of (nondegenerate) bounded random variables such that the Central Limit Theorem fails to hold. The sequence is in part an adaptation of a nonstationary example...

The on-line nearest-neighbour graph on a sequence of n uniform random points in (0,1)d () joins each point after the first to its nearest neighbour amongst its predecessors. For the total power-weighted edge-length of this graph, with weight exponent [alpha][set membership, variant](0,d/2], we...

Consider a near-integrated time series driven by a heavy-tailed and long-memory noise , where {[eta]j} is a sequence of i.i.d random variables belonging to the domain of attraction of a stable law with index [alpha]. The limit distribution of the quantile estimate and the semi-parametric...

We study a type of one-dimensional wave equation on the plane with non-linear random forcing. We are interested in the almost sure behaviour of the normalized increments of the solution process associated to this type of wave equation. Also we study the behaviour of the normalized increments of...

Let [sigma](t,t') be the sigma-algebra generated by the differences Xs-Xs' with s,s'[set membership, variant](t,t'), where (Xt)-[infinity]t[infinity] is the fractional Brownian motion with Hurst index H[set membership, variant](0,1). We prove that for any two distinct timepoints t1 and t2 the...