Invariant Measures and Symmetry Property of Lévy Type Operators

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Approximation of stable law in Wasserstein-1 distance by Stein’s method (2017, background): “6) therein (note that the linear operator in [2] is L = αA), we get μ is the unique invariant measure of A in the sense that ∫”
Criteria for ergodicity of Lévy type operators in dimension one (2008, methodology): “The idea of using Fourier analysis comes from [1].”
Exponential ergodicity and regularity for equations with Lévy noise (2011, unknown): “R (cos y − 1) dy |y|1+α ; see [35] and [3].”
Perturbations of Generalized Mehler Semigroups and Applications to Stochastic Heat Equations with Levy Noise and Singular Drift (2004, unknown): “dim E 1 , 10, 11, 13, 21] and references therein).”
Delay differential equations driven by Lévy processes: Stationarity and Feller properties (2005, background): “Invariant measures for ordinary differential equations with a nonlinear drift term and additive stable noise have been studied analytically by Albeverio, Rüdiger and Wu [1], but our general results, even when specified to the non-delayed case, seem to be new.”