论文标题
有界域中的征费过程：路径反射方案和监禁的签名
Levy processes in bounded domains: Path-wise reflection scenarios and signatures of confinement
论文作者
论文摘要
我们讨论了各种（途径）反射的影响 - 屏障场景限制了对称$α$稳定的lévy流程的范式属性的特性，该过程的永久居住在线中的永久居住在线被两边的反射确保了。根据特定的反射“机制”，推断的跳跃过程的光谱和统计特征有所不同，例如间隔中不变特性和不变（平衡或渐近近平衡）概率密度函数的功能形状。该分析是通过试图赋予反射莱维过程概念的尝试的，就其运动发生器的域而言，不变的pdf（实际上是特征功能）确实属于该概念。
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $α$-stable Lévy processes, whose permanent residence in a finite interval on a line is secured by a two-sided reflection. Depending on the specific reflection "mechanism", the inferred jump-type processes differ in their spectral and statistical characteristics, like e.g. relaxation properties, and functional shapes of invariant (equilibrium, or asymptotic near-equilibrium) probability density functions in the interval. The analysis is carried out in conjunction with attempts to give meaning to the notion of a reflecting Lévy process, in terms of the domain of its motion generator, to which an invariant pdf (actually an eigenfunction) does belong.
