Stochastic methods for the neutron transport equation II: Almost sure growth
Stochastic methods for the neutron transport equation II: Almost sure growth
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DOI：
10.1214/20-aap1574
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
S. Harris;E. Horton;A. Kyprianou
中科院分区：
文献类型：
--
作者：
S. Harris;E. Horton;A. Kyprianou
中子输运方程(NTE)描述了当核裂变过程活跃时，在非均匀裂变介质中穿过平面截面的中子通量。关于NTE的经典工作出现在20世纪50年代的应用数学文献中，通过R.Dauray和合作者的工作，[7，8，19]。当被设想为随机过程时，NTE还具有通过基本物理过程的半群的概率表示；[7、17、18、20]。最近，[6]和[16]继续了对NTE的概率分析，从空间分支过程和准平稳分布理论中引入了更新的概念。在这篇文章中，我们继续沿用相同的思路，并查看超临界状态下随机增长的基本描述。我们的主要结果比[20]中最后一次已知的对物理过程的生长性质的贡献提供了显著的改进，使中子输运理论与现代分支过程理论如[14，12]一致。
The neutron transport equation (NTE) describes the flux of neutrons across a planar cross-section in an inhomogeneous fissile medium when the process of nuclear fission is active. Classical work on the NTE emerges from the applied mathematics literature in the 1950s through the work of R. Dautray and collaborators, [7, 8, 19]. The NTE also has a probabilistic representation through the semigroup of the underlying physical process when envisaged as a stochastic process; cf. [7, 17, 18, 20]. More recently, [6] and [16] have continued the probabilistic analysis of the NTE, introducing more recent ideas from the theory of spatial branching processes and quasi-stationary distributions. In this paper, we continue in the same vein and look at a fundamental description of stochastic growth in the supercritical regime. Our main result provides a significant improvement on the last known contribution to growth properties of the physical process in [20], bringing neutron transport theory in line with modern branching process theory such as [14, 12].