Some known inequalities concerning p-variations and conditional p-variations for discrete parameter martingales are sharpened and carried over in the more general context.

This paper addresses the impact of time fluctuations of a random medium on refocusing during a time-reversal experiment. Even in the presence of moderate time perturbations a coherent refocused pulse is observed. The theory predicts the level of recompression observed as well as the conditions...

We consider the rate of convergence of the paths of some self-attracting diffusions. We prove that these diffusions are attracted by their mean-process. Moreover, under some assumptions on the interaction function f, this attraction becomes strong enough to imply the almost sure convergence of...

Stochastic partial differential equations with variable coefficients are considered in C1 domains. Existence and uniqueness results are given in Sobolev spaces with weights allowing the derivatives of the solutions to blow up near the boundary. The number of derivatives of the solution can be...

Completing previous results, we construct, for every , explicit examples of nearest neighbour random walks on the nonnegative integer line such that s is the scaling exponent of the associated random walk in random scenery for square integrable i.i.d. sceneries. We use coupling techniques to...

Assume that a compound Poisson surplus process is invested in a stochastic interest process which is assumed to be a Lévy process. We derive recursive and integral equations for ruin probabilities with such an investment. Lower and upper bounds for the ultimate ruin probability are obtained...

In this note we prove Hölder-type inequalities for products of certain functionals of correlated Brownian motions. These estimates are applied to the study of optimal portfolio choice in incomplete markets when the investor's utility is of the form U(X,Y)=g(X)h(Y), where X is the investor's...

For the model of directed polymers in a Gaussian random environment introduced by Imbrie and Spencer, we establish: - a Large Deviations Principle for the end position of the polymer under the Gibbs measure;- a scaling inequality between the volume exponent and the fluctuation exponent of the...

In this paper we study the convergence rate of the numerical approximation of the quantiles of the marginal laws of (Xt), where (Xt) is a diffusion process, when one uses a Monte Carlo method combined with the Euler discretization scheme. Our convergence rate estimates are obtained under two...

Let Xt be n-dimensional diffusion process and St be a smooth set-valued function. Suppose Xt is invisible when Xt[set membership, variant]St, but we can see the process exactly otherwise. Let Xt0[set membership, variant]St0 and we observe the process from the beginning till the signal reappears...