Non-local conservation law from stochastic particle systems

DOI10.1007/s10884-017-9620-4zbMath1427.60139arXiv1701.04677OpenAlexW2576821331MaRDI QIDQ1616368

Christian Olivera, Marielle Simon

Publication date: 6 November 2018

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.04677

zbMATH Keywords

stochastic differential equationsLévy processparticle systemsfractal conservation lawsemi-group approach

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Markov semigroups and applications to diffusion processes (47D07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Weak solutions to PDEs (35D30)

Related Items (5)

Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel ⋮ Recent progress on limit theorems for large stochastic particle systems ⋮ Uniform Approximation of 2 Dimensional Navier--Stokes Equation by Stochastic Interacting Particle Systems ⋮ Kinetic solutions for nonlocal stochastic conservation laws ⋮ Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise

Cites Work

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• Pathwise uniqueness for singular SDEs driven by stable processes
• Entropy formulation for fractal conservation laws
• A propagation of chaos result for a system of particles with moderate interaction
• Propagation of chaos and fluctuations for a moderate model with smooth initial data
• A probabilistic approach for nonlinear equations involving the fractional Laplacian and a singular operator
• Martingale and stationary solutions for stochastic Navier-Stokes equations
• Existence of strong solutions for Itô's stochastic equations via approximations
• Scaling limits for interacting diffusions
• Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators
• \(L^p\)-maximal regularity of nonlocal parabolic equations and applications
• Probabilistic approximation and inviscid limits for one-dimensional fractional conservation laws
• Fractal first-order partial differential equations
• General Fractal Conservation Laws Arising from a Model of Detonations in Gases
• A law of large numbers for moderately interacting diffusion processes
• Stochastic Equations in Infinite Dimensions
• Lévy Processes and Stochastic Calculus
• Instabilities and Nonlinear Patterns of Overdriven Detonations in Gases
• An introduction to continuous-time stochastic processes. Theory, models, and applications to finance, biology, and medicine

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