Stochastic Differential Geometry: An Introduction

Wilfrid S. Kendall
Additional contact information
Wilfrid S. Kendall: Strathclyde University, Department of Mathematics

A chapter in Stochastic and Integral Geometry, 1987, pp 29-60 from Springer

Abstract: Abstract Stochastic calculus can be used to provide a satisfactory theory of random processes on differentiable manifolds and, in particular, a description of Brownian motion on a Riemannian manifold which lends itself to constructions generalizing the classical development of smooth paths on a manifold. An introduction to this theory is given, and a survey is made of the relationship between curvature properties of the manifold and the asymptotic behaviour of the Brownian motion on the manifold. It is then explained how these results can be used to prove geometrical theorems concerning special classes of maps between manifolds.

Keywords: 58G32; 60J65; 60H10.; Semimartingale; Γ-martingale; Brownian motion on a manifold; geodesic; connection; parallel transport; stochastic lift; sectional curvature; Ricci curvature; harmonic map (search for similar items in EconPapers)
Date: 1987
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3921-9_3

Ordering information: This item can be ordered from
http://www.springer.com/9789400939219

DOI: 10.1007/978-94-009-3921-9_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().