Canonical Brownian motion on the space of univalent functions and resolution of Beltrami equations by a continuity method along stochastic flows

DOI10.1016/j.matpur.2004.06.001zbMath1061.60085OpenAlexW2106507609MaRDI QIDQ1887187

Anton Thalmaier, Paul Malliavin, Hélène Airault

Publication date: 23 November 2004

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2004.06.001

zbMATH Keywords

Jordan curvesconformal geometrystochastic flowunivalent functionsBeltrami equationBeurling-Ahlfors extensioncanonical Brownian motiondiffeomorphisms on the circlestochastic conformal welding

Mathematics Subject Classification ID

Brownian motion (60J65) Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (13)

Continuity modulus of stochastic homeomorphism flows for SDEs with non-Lipschitz coefficients ⋮ Riemannian geometry of \(\text{Diff}(S^{1})/S^{1}\) ⋮ Quasi-invariance of Brownian measures on the group of circle homeomorphisms and infinite-dimensional Riemannian geometry ⋮ Brownian measures on Jordan-Virasoro curves associated to the Weil-Petersson metric ⋮ Random conformal weldings ⋮ Random curves by conformal welding ⋮ Möbius transformations and extended diffusion above the homeomorphisms of the disk ⋮ Homeomorphic flows for multi-dimensional SDEs with non-Lipschitz coefficients ⋮ Entropic measure and Wasserstein diffusion ⋮ Hyperbolic measures, moments and coefficients. Algebra on hyperbolic functions ⋮ Invariant or quasi-invariant probability measures for infinite dimensional groups. II: Unitarizing measures or Berezinian measures ⋮ Riemannian connections and curvatures on the universal Teichmüller space ⋮ Freidlin-Wentzell's large deviations for homeomorphism flows of non-Lipschitz SDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The boundary correspondence under quasiconformal mappings
• A comparison theorem for solutions of stochastic differential equations and its applications
• Geometric approach to discrete series of unirreps for Vir
• Realization of Virasoro unitarizing measures on the set of Jordan curves.
• On a type of stochastic differential equations driven by countably many Brownian motions
• Stochastic flows for SDEs with non-Lipschitz coefficient.
• A class of stochastic differential equations with non-Lipschitzian coefficients: Pathwise uniqueness and no explosion
• Removability theorems for Sobolev functions and quasiconformal maps
• Unitarizing probability measures for representations of Virasoro algebra
• Analyticity of intersection exponents for planar Brownian motion
• Support of Virasoro unitarizing measures.
• 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.
• Generalized conformal welding
• On conformal welding homeomorphisms associated to Jordan curves
• The canonic diffusion above the diffeomorphism group of the circle

This page was built for publication: Canonical Brownian motion on the space of univalent functions and resolution of Beltrami equations by a continuity method along stochastic flows