Regularity of solutions to differential equations with non-Lipschitz coefficients

DOI10.1016/j.bulsci.2007.05.003zbMath1154.34025OpenAlexW2046676354MaRDI QIDQ924910

De Jun Luo

Publication date: 29 May 2008

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2007.05.003

zbMATH Keywords

regularitystochastic differential equationsHausdorff dimensiontransport equationnon-Lipschitz coefficientsgenerated flowspush-forward Lebesgue measure

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Ordinary differential equations and systems with randomness (34F05)

Related Items (5)

Pathwise uniqueness of multi-dimensional stochastic differential equations with Hölder diffusion coefficients ⋮ On the stochastic flow generated by the one default model in one-dimensional case ⋮ Legendre wavelet method for fractional delay differential equations ⋮ Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient ⋮ Nonexplosion and pathwise uniqueness of stochastic differential equation driven by continuous semimartingale with non-Lipschitz coefficients

Cites Work

• Transport equation and Cauchy problem for BV vector fields
• Global flows for stochastic differential equations without global Lipschitz conditions
• Ordinary differential equations, transport theory and Sobolev spaces
• Canonical Brownian motion on the diffeomorphism group of the circle
• Modulus of continuity of the canonic Brownian motion ``on the group of diffeomorphisms of the circle
• Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
• A study of a class of stochastic differential equations with non-Lipschitzian coefficients
• Flows associated with irregular \(\mathbb R^d\)-vector fields
• The canonic diffusion above the diffeomorphism group of the circle
• Unnamed Item
• Unnamed Item

This page was built for publication: Regularity of solutions to differential equations with non-Lipschitz coefficients