Levy targeting and the principle of detailed balance

Abstract

We investigate confined Lévy flights under premises of the principle of detailed balance. The master equation admits a transformation to Lévy - Schrödinger semigroup dynamics (akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation). We solve a stochastic targeting problem for arbitrary stability index $0<\mu <2$ of Lévy drivers: given an invariant probability density function (pdf), specify the jump - type dynamics for which this pdf is a long-time asymptotic target. Our ("$\mu$-targeting") method is exemplified by Cauchy family and Gaussian target pdfs. We solve the reverse engineering problem for so-called Lévy oscillators: given a quadratic semigroup potential, find an asymptotic pdf for the associated master equation for arbitrary $\mu$.

References in corpus (3)

• Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
• Stationary states in single-well potentials under symmetric Levy noises
• Heavy-tailed targets and (ab)normal asymptotics in diffusive motion

Cited by in corpus (11)

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• Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well
• Lévy flights in the infinite potential well as the hypersingular Fredholm problem
• Lévy flights confinement in a parabolic potential and fractional quantum oscillator
• Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
• Peculiarities of escape kinetics in the presence of athermal noises
• Levy flights in steep potential wells: Langevin modeling versus direct response to energy landscapes
• Nonlinear friction in underdamped anharmonic stochastic oscillators
• Levy flights in confining environments: Random paths and their statistics
• Stochastic kinetics under combined action of two noise sources
• Thermalization of Levy flights: Path-wise picture in 2D