Pathwise uniqueness for a degenerate stochastic differential equation

DOI10.1214/009117907000000033zbMath1139.60027arXivmath/0601505OpenAlexW2074098349WikidataQ115240900 ScholiaQ115240900MaRDI QIDQ2460330

Zhen-Qing Chen, Krzysztof Burdzy, Richard F. Bass

Publication date: 14 November 2007

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

Full work available at URL: https://arxiv.org/abs/math/0601505

zbMATH Keywords

stochastic differential equationsweak uniquenesspathwise uniquenessstrong uniqueness

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60)

Related Items (13)

Stationary distributions for diffusions with inert drift ⋮ Stochastic flows and Bismut formulas for stochastic Hamiltonian systems ⋮ The submartingale problem for a class of degenerate elliptic operators ⋮ On the martingale problem for degenerate-parabolic partial differential operators with unbounded coefficients and a mimicking theorem for Itô processes ⋮ A jump-type SDE approach to real-valued self-similar Markov processes ⋮ Stability problems for Cantor stochastic differential equations ⋮ The Dynamics of Instability ⋮ Strong uniqueness for an SPDE via backward doubly stochastic differential equations ⋮ On the Euler–Maruyama Scheme for Degenerate Stochastic Differential Equations with Non-sticky Condition ⋮ Pathwise nonuniqueness for the SPDEs of some super-Brownian motions with immigration ⋮ Existence and uniqueness of degenerate SDEs with Hölder diffusion and measurable drift ⋮ Stratonovich stochastic differential equation with irregular coefficients: Girsanov's example revisited ⋮ Measure-valued flows given consistent exchangeable families

Cites Work

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• On one-dimensional stochastic differential equations with non-sticky boundary conditions
• Uniqueness for reflecting Brownian motion in Lip domains
• On the uniqueness of solutions of stochastic differential equations
• On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations
• On solutions of one-dimensional stochastic differential equations without drift
• One Dimensional Stochastic Differential Equations with No Strong Solution
• Stochastic Integrals of Continuous Local Martingales, II
• Diffusions and Elliptic Operators

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