Construction of program control with probability one for a dynamical system with Poisson perturbations

On Stein's method and perturbations

Stein's (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Stein's method, one needs to establish a Stein identity for the approximating distribution, solve the Stein equation and estimate the behaviour of the solutions in terms of the metrics under study. For some Stein equations, solutions with good properties are known; for others, this is not the case. Barbour and Xia (1999) introduced a perturbation method for Poisson approximation, in which Stein identities for…

Integrated density of states for Poisson-Schrödinger perturbations of subordinate Brownian motions on the Sierpiński gasket

We prove the existence of the integrated density of states for subordinate Brownian motions in presence of the Poissonian random potentials on the Sierpiński gasket.

泊松过程扰动公式在初等和几何概率中的应用

Applications of the perturbation formula for Poisson processes to elementary and geometric probability

本文通过泊松过程的扰动公式，统一推导了多种分布的积分表示，并提出新的积分微分恒等式，同时扩展了克罗夫特顿导数公式以适用于泊松过程及二项点过程。

Perturbation analysis of Poisson processes

We consider a Poisson process $Φ$ on a general phase space. The expectation of a function of $Φ$ can be considered as a functional of the intensity measure $λ$ of $Φ$. Extending earlier results of Molchanov and Zuyev [Math. Oper. Res. 25 (2010) 485-508] on finite Poisson processes, we study the behaviour of this functional under signed (possibly infinite) perturbations of $λ$. In particular, we obtain general Margulis-Russo type formulas for the derivative with respect to non-linear transformations of the intensity measure depending on some parameter. As an application, we study the behaviour …

泊松超平面镶嵌零胞在方向扰动下的Wasserstein稳定性

Wasserstein stability of the zero cell of a Poisson hyperplane tessellation under directional perturbations

该研究分析泊松超平面镶嵌零胞在方向分布扰动下的Wasserstein稳定性，给出其局部Hölder连续性的定量界，并将结果应用于界定零胞密度估计器的期望总变差距离。

Stabilization of stochastic dynamical systems of a random structure with Markov switches and Poisson perturbations

An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes the system stable in probability. Sufficient conditions of the stability in probability are obtained, using the second Lyapunov method, in which the construction of the corresponding functions plays an important role. Here we provide a solution to the problem of optimal stabilization in a general case. For a linear system with a quadratic quality fu…