Asymptotic behaviour of stochastic flows of diffeomorphisms: Two case studies

DOI10.1007/BF01845993zbMath0592.60044OpenAlexW2075448167MaRDI QIDQ1075695

Peter H. Baxendale

Publication date: 1986

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01845993

zbMATH Keywords

Lyapunov exponentsstochastic flowsBrownian pathslocal and global stabilityin hyperbolic spaceof the flowstochastic parallel translation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Diffusion processes and stochastic analysis on manifolds (58J65) Geodesic flows in symplectic geometry and contact geometry (53D25) Ergodic theory (37A99) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (13)

Stochastic flows on the boundaries of \(\text{SL}(n,\mathbb{R})\) ⋮ Ergodicity of a measure-valued Markov chain induced by random transformations ⋮ Estimates for the volume variation of compact submanifolds driven by a stochastic flow ⋮ DYNAMICAL PROPERTIES OF LÉVY PROCESSES IN LIE GROUPS ⋮ Lyapunov exponents and relative entropy for a stochastic flow of diffeomorphisms ⋮ Lyapunov exponents of stochastic flows ⋮ Stochastic flows on the boundaries of lie groups ⋮ Limiting points of stochastic flows ⋮ Lévy processes in semisimple Lie groups and stability of stochastic flows ⋮ The Brownian Motion and the Canonical Stochastic Flow on a Symmetric Space ⋮ Lyapunov Exponents for a Stochastic Analogue of the Geodesic Flow ⋮ Characterising stochastic fixed points and limit cycles for dynamical systems with additive noise ⋮ Spectral expansion of the occupation measure for birth and death on a flow

Cites Work

• Mécanique aléatoire
• On backward stochastic differential equations
• Flows of stochastic dynamical systems: ergodic theory
• Recurrence of a Diffusion Process to a Shrinking Target
• Wiener processes on manifolds of maps
• A classification of the second order degenerate elliptic operators and its probabilistic characterization
• Riemann-Stieltjes approximations of stochastic integrals
• Riemannian geometry
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