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Stochastic parallel displacement

Part of the Lecture Notes in Mathematics book series (LNM,volume 451)

Keywords

  • Brownian Motion
  • Riemannian Manifold
  • Orthonormal Basis
  • Stochastic Differential Equation
  • Covariant Vector

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Bibliography

  1. K. Itô, Stochastic differentials, to appear in Applied Mathematics and optimization.

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  2. K. Itô, The Brownian motion and tensor fields on Riemannian manifold, Proc. Int. Congress Math. 1962 (Stockholm), 536–539.

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  3. E.B. Dynkin, Diffusions of tensors, Soviet Math. Dokl. Vol. 9 (1968), No. 2, 532–535.

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  4. H.P. McKean, Jr., Brownian motions on the 3-dimensional rotation group, Mem. Coll. Sci., Univ. Kyoto, Ser. A, 33, Math. No. 1 (1960), 25–38.

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  5. R.L. Stratonovich, Conditional Markov processes and their application to optimal control, Elsevier, New York (1968).

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  6. D.L. Fisk, Quasi-martingales and stochastic integrals, Technical Report No. 1, Dept. of Math., Michigan State University, 1963.

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© 1975 Springer-Verlag

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Itô, K. (1975). Stochastic parallel displacement. In: Pinsky, M.A. (eds) Probabilistic Methods in Differential Equations. Lecture Notes in Mathematics, vol 451. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068575

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  • DOI: https://doi.org/10.1007/BFb0068575

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07153-2

  • Online ISBN: 978-3-540-37481-7

  • eBook Packages: Springer Book Archive