Fractional diffusion limit for a kinetic equation with an interface

DOI10.1214/20-AOP1423zbMath1452.35212arXiv1905.10586OpenAlexW3005127444MaRDI QIDQ2212594

Stefano Olla, Tomasz Komorowski, Leonid Ryzhik

Publication date: 24 November 2020

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.10586

zbMATH Keywords

stable processesfractional Laplacianboundary conditions at interfacediffusion limits from kinetic equations

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Linear integral equations (45A05) Fractional partial differential equations (35R11) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Jump processes on general state spaces (60J76)

Related Items (6)

Diffusion approximation for a simple kinetic model with asymmetric interface ⋮ Derivation of anomalous behavior from interacting oscillators in the high-temperature regime ⋮ Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion ⋮ Pairs of complementary transmission conditions for Brownian motion ⋮ Quantitative fluid approximation in transport theory: a unified approach ⋮ Thermal boundaries in kinetic and hydrodynamic limits

Cites Work

• Unnamed Item
• Unnamed Item
• Anomalous diffusion phenomena: a kinetic approach
• Suprema of Lévy processes
• Fractional diffusion limit for collisional kinetic equations: a Hilbert expansion approach
• Fractional diffusion limit for collisional kinetic equations
• Energy transport in stochastically perturbed lattice dynamics
• Limit theorems for additive functionals of a Markov chain
• Linear Boltzmann equation and fractional diffusion
• Fractional diffusion limits of non-classical transport equations
• Anomalous diffusion limit of kinetic equations in spatially bounded domains
• High frequency limit for a chain of harmonic oscillators with a point Langevin thermostat
• Fractional diffusion limit of a kinetic equation with diffusive boundary conditions in the upper-half space
• Diffusion limit for a kinetic equation with a thermostatted interface
• Introductory lectures on fluctuations of Lévy processes with applications.
• On some relations between the harmonic measure and the Levy measure for a certain class of Markov processes
• Stochastic-Process Limits
• Limit theorems for some continuous-time random walks
• Exit Properties of Stochastic Processes with Stationary Independent Increments
• An Invariance Principle in Renewal Theory
• Convergence of a kinetic equation to a fractional diffusion equation

This page was built for publication: Fractional diffusion limit for a kinetic equation with an interface