Relaxation patterns and semi-Markov dynamics

Mark M. Meerschaert and Bruno Toaldo

Stochastic Processes and their Applications, 2019, vol. 129, issue 8, 2850-2879

Abstract: Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variety of relaxation patterns. Power law relaxation is related to fractional derivatives in the time variable. More general relaxation patterns are considered here, and the corresponding semi-Markov processes are studied. Our method, based on Bernstein functions, unifies three different approaches in the literature.

Keywords: Relaxation; Fractional calculus; Bernstein function; Semi-Markov process; Continuous time random walk; Semigroup (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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DOI: 10.1016/j.spa.2018.08.004

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