Stochastic differential geometry: An introduction

DOI10.1007/BF00580820zbMath0629.60087OpenAlexW4254139370WikidataQ115394980 ScholiaQ115394980MaRDI QIDQ1094002

Wilfrid S. Kendall

Publication date: 1987

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00580820

zbMATH Keywords

surveyMalliavin calculusRicci curvaturestochastic flowsWiener sausagesasymptotic properties of semi-martingalesBrownian coupling propertyBrownian motion on a Riemannian manifoldcurvature properties of the manifoldstochastic differential formsstochastic Kählerian geometrytransience and recurrence

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Generalizations of martingales (60G48) Diffusion processes and stochastic analysis on manifolds (58J65) Martingales and classical analysis (60G46)

Related Items

Stochastic calculus, statistical asymptotics, Taylor strings and phyla ⋮ Rigidity for Markovian maximal couplings of elliptic diffusions ⋮ The Brownian traveller on manifolds ⋮ Stochastic thermodynamics of holonomic systems ⋮ Representation of Radon shape diffusions via hyperspherical Brownian motion ⋮ Semimartingales and geometric inequalities on locally symmetric manifolds ⋮ Statistical mechanics of holonomic systems as a Brownian motion on smooth manifolds ⋮ Coupled Brownian motions and partial domain monotonicity for the Neumann heat kernel

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Function theory on manifolds which possess a pole
• Function theory, random paths and covering spaces
• \(L^ p\) and mean value properties of subharmonic functions on Riemannian manifolds
• Convergence of martingales on a Riemannian manifold
• Large deviations and the Malliavin calculus
• On conformal martingale diffusions and pluripolar sets
• The Atiyah-Singer theorems: A probabilistic approach. I: The index theorem
• The Dirichlet problem at infinity for manifolds of negative curvature
• The Dirichlet problem at infinity for a negatively curved manifold
• Winding of the plane Brownian motion
• Stochastic intersection number and homological behaviors of diffusion processes on Riemannian manifolds
• Brownian motion and random walks on manifolds
• Brownian motion, geometry, and generalizations of Picard's little theorem
• Convergence of martingales on manifolds of negative curvature
• Positive harmonic functions on complete manifolds of negative curvature
• Coupling of multidimensional diffusions by reflection
• Comparison theorems for Brownian motions on Riemannian manifolds and their applications
• The radial part of Brownian motion on a manifold: A semimartingale property
• Formules de la moyenne, calcul de perturbations et théoremes d'annulation pour les formes harmoniques
• Mappings of bounded dilatation of Riemannian manifolds
• Harmonic morphisms between Riemannian manifolds
• Théoremes de comparaison en géométrie Riemannienne
• On the heat kernel of a complete Riemannian manifold
• On a comparison theorem for solutions of stochastic differential equations and its applications
• Flows of stochastic dynamical systems: The functional analytic approach
• Random walk on a sphere and on a Riemannian manifold
• Entropy Via Random Perturbations
• The asymptotic joint distribution of windings of planar Brownian motion
• On the convergence of gangolli processes to brownian motion on a manifold
• Curvature, geodesics and the Brownian motion on a Riemannian manifold I—Recurrence properties
• Approximating Ito integrals of differential forms and geodesic deviation
• Brownian Motion on a Hypersurface
• Stochastic Differential Geometry, a Coupling Property, and Harmonic Maps
• Nonnegative ricci curvature and the brownian coupling property
• The geometry of random genetic drift VI. A random selection diffusion model
• Wiener processes on manifolds of maps
• Picard's Theorem and Brownian Motion
• Behavior of diffusion semi-groups at infinity
• DIFFUSION PROCESSES AND RIEMANNIAN GEOMETRY
• Brownian Motion and Harmonic Functions on Manifolds of Negative Curvature
• A Report on Harmonic Maps
• Diffusion processes in a small time interval
• Brownian Motions of Ellipsoids
• The limiting angle of certain riemannian brownian motions
• Brownian Motion and a Generalised Little Picard's Theorem
• Electrostatic capacity, heat flow, and brownian motion
• On the construction of certain diffusions on a differentiable manifold
• Brownian Motion on the Surface of the 3-Sphere