We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time 1 value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its associated optimal trading strategy for the insider. In the equilibrium the ins...

We define a family of SLE-type processes in finitely connected domains, which are called continuous LERW (loop-erased random walk). A continuous LERW describes a random curve in a finitely connected domain that starts from a prime end and ends at a certain target set, which could be an interior point, or a prime end, or a side arc. It is defined using the usual chordal Loewner equation with the...

We consider some non-homogeneous Poisson models to estimate the mean number of times that a given environmental threshold of interest is surpassed by a given pollutant. Seven different rate functions for the Poisson processes describing the models are taken into account. The rate functions considered are the Weibull, exponentiated-Weibull, and their generalisation the Beta-Weibull rate function...

We study charge screening in a system of two dimensional nonabelian vortices, at finite temperature. Such vortices are generated after an SO(3) global symmetry group is spontaneously broken to a discrete subgroup Q8, where the latter is isomorphic to the nonabelian group of quaternions. Poisson-Boltzmann like equations are derived for the various inter-vortex potentials, and the solutions to lo...

Abstract Shnerb et al. (2000), (2001) studied the following system of interacting particles on Z: There are two kinds of particles, called A-particles and B-particles. The A-particles perform continuous time simple random walks, independently of each other. The jumprate of each A-particle is DA. The B-particles perform continuous time simple random walks with jumprate DB , but in addition they ...

We consider an inverse problem for determining an inhomogeneity in a viscoelastic body of the Zener type, using Cauchy boundary data, under cyclic loads at low frequency. We show that the inverse problem reduces to the one for the Helmholtz equation and to the same nonlinear Calderon equation given for the harmonic case. A method of solution is proposed which consists in two steps : solution of...

In this paper we present the solution to a longstanding problem of differential geometry: Lie’s third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrability by local Lie groupoids, we clarify the smoothness of the Poisson sigma-mode...

The problem of computing the electrostatic energy of a large molecule is considered. It is reduced to solving the Poisson equation inside the domain and the linear Poisson-Boltzmann equation in the exterior, coupled by boundary conditions. Monte Carlo estimates for the potential point values, their derivatives, and the energy are constructed. These estimates are based on the walk on spheres and...

In this paper, we formulate the problem of natural image matting as one of solving Poisson equations with the matte gradient field. Our approach, which we call Poisson matting, has the following advantages. First, the matte is directly reconstructed from a continuous matte gradient field by solving Poisson equations using boundary information from a user-supplied trimap. Second, by interactivel...

We investigate the possible effect of the residual annihilations of heavy particles after freeze-out from equilibrium in the early universe. An error in previous work on this subject is pointed out and the correct method of solving the Boltzmann equation for this case is developed. For Majorana particles there are significant differences relative to previous work. PACS: 98.80.Cq, 95.35.+d, 95.3...