On the influence of reflective boundary conditions on the statistics of Poisson–Kac diffusion processes

Massimiliano Giona, Antonio Brasiello and Silvestro Crescitelli

Physica A: Statistical Mechanics and its Applications, 2016, vol. 450, issue C, 148-164

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.

Keywords: Diffusion; Poisson–Kac process; Hyperbolic stochastic models; Transport on fractals; Emerging statistical properties (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:450:y:2016:i:c:p:148-164

DOI: 10.1016/j.physa.2015.12.142

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