Abstract
A method for constructing measures on spaces of paths in compact Riemannian manifolds embedded in Euclidean space is developed. For measures obtained by this way, a Cameron-Martin-Girsanov-Maruyama-Ramer transformation formula is obtained. A particular case of this formula is the formula for transformations of the measures describing Brownian motion on compact Riemannian manifolds.
Mathematics Subject Classification (1991): 60H07, 60H05, 60H10, 60H15, 60J25.
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Smolyanov, O.G. (1998). Change of Variable Formulas for Gaussian Integrals over Spaces of Paths in Compact Riemannian Manifolds. In: Komrakov, B.P., Krasil’shchik, I.S., Litvinov, G.L., Sossinsky, A.B. (eds) Lie Groups and Lie Algebras. Mathematics and Its Applications, vol 433. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5258-7_27
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DOI: https://doi.org/10.1007/978-94-011-5258-7_27
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