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General sufficient conditions are given for absolute continuity and convergence in variation of the distributions of the unctionals on a probability space, generated by a Poisson point measure. The phase space of the Poisson point measure is supposed to be of the form (0,infty)times U, and its intensity measure to be equal dtPi(du). We introduce the family of time stretching transformations of the configurations of the point measure. The sufficient conditions for absolute continuity and convergence in variation are given in the terms of the time stretching transformations and the relative differential operators. These conditions are applied to solutions of SDEs driven by Poisson point measures, including an SDEs with non-constant jump rate.
Let $Omega subset mathbb{R}^{n+1}$ be an open set whose boundary may be composed of pieces of different dimensions. Assume that $Omega$ satisfies the quantitative openness and connectedness, and there exist doubling measures $m$ on $Omega$ and $mu$ o
We give a pathwise construction of a two-parameter family of purely-atomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson-Dirichlet$(alpha,theta)$ distributions, for $alphain (0,1)$ and $thetage 0$. This res
Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. Previous works, using the Steins method, give the convergence rate of a
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient condition fo
Given a vector $F=(F_1,dots,F_m)$ of Poisson functionals $F_1,dots,F_m$, we investigate the proximity between $F$ and an $m$-dimensional centered Gaussian random vector $N_Sigma$ with covariance matrix $Sigmainmathbb{R}^{mtimes m}$. Apart from findin