论文标题
分数动力学方程
Fractional kinetic equations
论文作者
论文摘要
我们将非马克维亚CTRW（连续时间随机步行）近似的概念发展到相互作用的粒子系统的演变，这导致了一般的分数动力学测量值估算的演变，并具有可变顺序。 我们证明了由此产生的新方程的良好性，并为其解决方案提供了概率公式。尽管我们的方法非常笼统，但为简单起见，我们仅详细处理相互作用扩散的分数版本。该论文可以被视为从贝拉夫金（Belavkin）和马斯洛夫（Maslov）的作品中发展的思想的发展，这些作品专门针对互动粒子的马尔可夫（量子和经典）系统。
We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to the evolution of interacting particle systems, which leads to a general class of fractional kinetic measure-valued evolutions with variable order. We prove the well-posedness of the resulting new equations and present a probabilistic formula for their solutions. Though our method are quite general, for simplicity we treat in detail only the fractional versions of the interacting diffusions. The paper can be considered as a development of the ideas from the works of Belavkin and Maslov devoted to Markovian (quantum and classical) systems of interacting particles.
