论文标题
从半马尔可夫随机演变到散射运输和超截止
From semi-Markov random evolutions to scattering transport and superdiffusion
论文作者
论文摘要
我们在这里研究了由一类半马科夫过程驱动的Banach空间的随机演变。这种发展的期望（从博切纳的意义上讲）证明可以解决一些抽象的库奇问题。此外，抽象电报（阻尼波）方程被推广到半马多夫扰动的情况下。特别关注的是可以通过这些演变来表示的半马尔可夫散射传输过程模型。特别是，我们考虑具有无限平均飞行时间的随机飞行，这些飞行是由线性玻尔兹曼方程的半马尔科夫概括所控制的。事实证明，它们的缩放限制融合到超级延伸的运输过程中。
We here study random evolutions on Banach spaces, driven by a class of semi-Markov processes. The expectation (in the sense of Bochner) of such evolutions is shown to solve some abstract Cauchy problems. Further, the abstract telegraph (damped wave) equation is generalized to the case of semi-Markov perturbations. A special attention is devoted to semi-Markov models of scattering transport processes which can be represented through these evolutions. In particular, we consider random flights with infinite mean flight times which turn out to be governed by a semi-Markov generalization of a linear Boltzmann equation; their scaling limit is proved to converge to superdiffusive transport processes.
