We show that under a 3+[delta] moment condition (where [delta]0) there exists a 'Hartman-Winter' Law of the iterated logarithm for random walks conditioned to stay non-negative. We also show that under a second moment assumption the conditioned random walk eventually grows faster than n1/2(log...

We study mild solutions u to the semilinear Cauchy problem with x[set membership, variant][0,1], f a nonnegative measurable function and [gamma] a positive constant. Solutions to this equation are given by , where is the log-Laplace semigroup of a supercritical superprocess taking values in the...

Let V(t,x), be a time-space stationary d-dimensional Markovian and Gaussian random field given over a probability space . Consider a diffusion with a random drift given by the stochastic differential equation , x(0)=0, where w(·) is a standard d-dimensional Brownian motion defined over...

In this paper, we introduce first a natural generalization of the concept of Dirichlet process, providing significant examples. The second important tool concept is the n-covariation and the related n-variation. The n-variation of a continuous process and the n-covariation of a vector of...

This paper investigates the probability of ruin within finite horizon for a discrete time risk model, in which the reserve of an insurance business is currently invested in a risky asset. Under assumption that the risks are heavy tailed, some precise estimates for the finite time ruin...

The paper is concerned with the first meeting or crossing problem between two independent trajectories for some basic counting processes. Our interest is focused on the exact distribution of the level and the time of this first meeting or crossing. The question is examined for a renewal process...

In this paper, we are interested in solving backward stochastic differential equations (BSDEs for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic calculus related to BSDEs. Then we derive a priori...

Among Lévy processes with unbounded variation, we distinguish the abrupt ones, which are characterised by infinitely sharp extrema. Stable processes with parameter [alpha]1 and creeping Lévy processes are abrupt. We give a characterisation of abrupt processes and study their Dini derivatives...

Let be an additive Lévy process in withwhere X1,...,XN are independent, classical Lévy processes on with Lévy exponents [Psi]1,...,[Psi]N, respectively. Under mild regularity conditions on the [Psi]i's, we derive moment estimates that imply joint continuity of the local times in question....

Large time annealed path measure limits for a one-dimensional Brownian motion, with possibly a small drift, moving among "soft" Poissonian traps are considered. Limits with respect to both scaled and unscaled motions are derived. The results in both cases considered here agree with those shown...