We investigate the typical sizes and shapes of sets of points obtained by irregularly tracking two-dimensional Brownian bridges. The tracking process consists of observing the path location at the arr...
A Poisson pencil is called flat if all brackets of the pencil can be simultaneously locally brought to a constant form. Given a Poisson pencil on a 3-manifold, we study under which conditions it is fl...
Sticks at one of different orientation are placed in an i.i.d. fashion at points of a Poisson point process of intensity $λ$. Sticks of the same direction have the same length, while sticks in differ...
A workload model using the infinite source Poisson model for bursts is combined with the on--off model for within burst activity. Burst durations and on--off durations are assumed to have heavy-tailed...
We calculate, in a relatively explicit way, the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces. A...
We propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large d...
We will find Green's function for the standard weighted Laplacian and use the corresponding Green's potential to solve Poisson's equation in the unit disc with zero boundary values, in the sense of ra...
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation
Physics of Optoelectronics focuses on the properties of optical fields and their interaction with matter. Understanding that lasers, LEDs, and photodetectors clearly exemplify this interaction, the au...
This paper contributes to the compactification approach to study mean-field control problems with Poissonian common noise. To overcome the lack of compactness and continuity issues caused by common no...
This paper studies mean-field control problems with state-control joint law dependence and Poissonian common noise. We develop the stochastic maximum principle (SMP) and establish its connection to th...
Let X(Σ) be a smooth projective toric variety for a complex torus T_\C. In this paper, a real T_\C-invariant Poisson structure Π_Σis constructed on the complex manifold X(Σ), the symplectic leaves...
Let X be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X, and let \g denote the complexification of th...
Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed
