Spatial asymptotic behavior of homeomorphic global flows for non-Lipschitz SDEs

DOI10.1016/j.bulsci.2006.12.001zbMath1139.60324OpenAlexW2031566523MaRDI QIDQ2472853

Zongxia Liang

Publication date: 25 February 2008

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

Full work available at URL: https://doi.org/10.1016/j.bulsci.2006.12.001

zbMATH Keywords

non-Lipschitz conditionsGRR Lemmaspatial growth ratestochastic homeomorphic flow

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Asymptotic theory of functional-differential equations (34K25) Sample path properties (60G17) Ordinary differential equations and systems with randomness (34F05) Dynamics induced by flows and semiflows (37C10)

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ANTICIPATING MULTIDIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH REFLECTIONS

Cites Work

• Schilder theorem for the Brownian motion on the diffeomorphism group of the circle
• Global flows for stochastic differential equations without global Lipschitz conditions
• Inequalities for differential and integral equations
• Spatial estimates for stochastic flows in Euclidean space
• On a type of stochastic differential equations driven by countably many Brownian motions
• Existence and pathwise uniqueness of solutions for stochastic differential equations with respect to martingales in the plane
• On the spatial asymptotic behavior of stochastic flows in Euclidean space
• Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma, and applications to local times
• 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
• Integration of Brownian vector fields.
• Flows, coalescence and noise.
• Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory
• Homeomorphic property of solutions of SDE driven by countably many Brownian motions with non-Lipschitzian coefficients
• Homeomorphic flows for multi-dimensional SDEs with non-Lipschitz coefficients
• The canonic diffusion above the diffeomorphism group of the circle

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