On the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes
arXiv:1507.08851 · doi:10.1016/j.physa.2015.12.142
Abstract
We analyze the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes, and specifically how they modify the Poissonian switching-time statistics. After addressing simple cases such as diffusion in a channel, and the switching statistics in the presence of a polarization potential, we thoroughly study Poisson-Kac diffusion in fractal domains. Diffusion in fractal spaces highlights neatly how the modification in the switching-time statistics associated with reflections against a complex and fractal boundary induces new emergent features of Poisson-Kac diffusion leading to a transition from a regular behavior at shorter timescales to emerging anomalous diffusion properties controlled by walk dimensionality of the fractal set.
References in corpus (1)
Cited by in corpus (3)
- Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part I Basic theory
- Extended Poisson-Kac theory: A unifying framework for stochastic processes with finite propagation velocity
- Markovian nature, completeness, regularity and correlation properties of Generalized Poisson-Kac processes