We present and discuss connections between the problem of trend to equilibrium for one-dimensional Fokker–Planck equations modeling socio-economic problems, and one-dimensional functional inequalities of the type of Poincaré, Wirtinger and logarithmic Sobolev, with weight, for probability densities with polynomial tails. As main examples, we consider inequalities satisfied by inverse Gamma densities, taking values on R+, and Cauchy-type densities, taking values on R.

One-Dimensional Fokker–Planck Equations and Functional Inequalities for Heavy Tailed Densities / G. Furioli, A. Pulvirenti, E. Terraneo, G. Toscani. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - 90:(2022 Jun), pp. 177-208. [10.1007/s00032-022-00352-3]

One-Dimensional Fokker–Planck Equations and Functional Inequalities for Heavy Tailed Densities

E. Terraneo;
2022

Abstract

We present and discuss connections between the problem of trend to equilibrium for one-dimensional Fokker–Planck equations modeling socio-economic problems, and one-dimensional functional inequalities of the type of Poincaré, Wirtinger and logarithmic Sobolev, with weight, for probability densities with polynomial tails. As main examples, we consider inequalities satisfied by inverse Gamma densities, taking values on R+, and Cauchy-type densities, taking values on R.
Fokker–Planck type equations; Kinetic equations; Logarithmic Sobolev inequalities with weight; Weighted Poincaré type inequalities; Weighted Wirtinger type inequalities
Settore MAT/05 - Analisi Matematica
28-mar-2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/927608
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