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Stochastic and Integral Geometry pp 29–60Cite as

Stochastic Differential Geometry: An Introduction

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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.

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  1. Department of Mathematics, Strathclyde University, Livingstone Tower, 26 Richmond Street, Glasgow, G1 1XH, Scotland

    Wilfrid S. Kendall

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  1. Wilfrid S. Kendall
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  1. Armenian Academy of Sciences, Yerevan, USSR

    R. V. Ambartzumian

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© 1987 D. Reidel Publishing Company

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Kendall, W.S. (1987). Stochastic Differential Geometry: An Introduction. In: Ambartzumian, R.V. (eds) Stochastic and Integral Geometry. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3921-9_3

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  • DOI: https://doi.org/10.1007/978-94-009-3921-9_3

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