论文标题
跳跃移动过程的伙伴和偏僻的特性，并应用于相互作用的粒子系统
Feller and ergodic properties of jump-move processes with applications to interacting particle systems
论文作者
论文摘要
我们认为马尔可夫的过程可以交替进行连续运动，并在一般紧凑的波兰空间中跳跃。从机械结构开始，本文的首要贡献是提供有关动力学的条件，从而使相关的过渡内核形成feller semigroup，并推断相应的无穷小发电机。在第二个贡献中，我们调查了跳跃由生育和死亡组成的特殊情况下的千古特性，在包括流行病学，生态学和微生物学在内的几种应用中观察到了这种情况。基于耦合参数，我们获得了收敛到固定度量的条件，并具有收敛的几何速率。在整篇文章中，我们通过与出生和死亡相互作用的颗粒系统的一般示例来说明我们的结果。我们表明，在某些情况下，固定度量可以显式，并对应于r d的紧凑子集上的吉布斯度量。我们的示例包括与排斥的Lennard-Jones潜力和Riesz电位相关的Gibbs度量。
We consider Markov processes that alternate continuous motions and jumps in a general locally compact polish space. Starting from a mechanistic construction, a first contribution of this article is to provide conditions on the dynamics so that the associated transition kernel forms a Feller semigroup, and to deduce the corresponding infinitesimal generator. In a second contribution, we investigate the ergodic properties in the special case where the jumps consist of births and deaths, a situation observed in several applications including epidemiology, ecology and microbiology. Based on a coupling argument, we obtain conditions for the convergence to a stationary measure with a geometric rate of convergence. Throughout the article, we illustrate our results by general examples of systems of interacting particles in R d with births and deaths. We show that in some cases the stationary measure can be made explicit and corresponds to a Gibbs measure on a compact subset of R d. Our examples include in particular Gibbs measure associated to repulsive Lennard-Jones potentials and to Riesz potentials.
