We work out a stationary process on the real line to represent the positions of the multiple cracks which are observed in some composites materials submitted to a fixed unidirectional stress [var epsilon]. Our model is the one-dimensional random sequential adsorption. We calculate the intensity...

By studying the local time of reflecting diffusion processes, explicit gradient estimates of the Neumann heat semigroup on non-convex manifolds are derived from a recent derivative formula established by Hsu. As an application, an explicit lower bound of the first Neumann eigenvalue is presented...

We prove that the generator g of a backward stochastic differential equation (BSDE) can be represented by the solutions of the corresponding BSDEs at point (t,y,z) if and only if t is a conditional Lebesgue point of generator g with parameters (y,z). By this conclusion, we prove that, if g is a...

In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths . Our techniques provide a...

Insider trading consists in having an additional information, unknown from the common investor, and using it on the financial market. Mathematical modeling can study such behaviors, by modeling this additional information within the market, and comparing the investment strategies of an insider...

This paper analyzes the probabilistic structure of Markov-switching GARCH(p,q) models, in which the volatility process is driven by a finite state-space Markov chain. We give necessary and sufficient conditions for the existence of moments of any order. We find that the squares and higher order...

We consider a tracer particle performing a nearest neighbor random walk on in dimension d[greater-or-equal, slanted]3 with random jump rates. This kind of a walk models the motion of a charged particle under a constant external electric field. We assume that the jump rates admit only two values...

In this paper we study the two-dimensional joint distribution of the first passage time of a constant level by spectrally negative generalized Ornstein-Uhlenbeck processes and their primitive stopped at this first passage time. By using martingales techniques, we show an explicit expression of...

In this article we discuss spatial couplings for measure-valued population models which have a particle representation. We will show that provided the corresponding genealogies are compact the qualitative behavior of a coupling of a particle's individual motion translates into a coupling of the...

This paper studies the problem of a company that adjusts its stochastic production capacity in reversible investments with controls of expansion and contraction. The company may also decide on the activation time of its production. The profit production function is of a very general form...