This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baxendale P. Measures and Markov processes on function spaces.-Bull. Soc. math. France, 1976, Mémoire 46.
Belopol’skaya Ya.I. and Daletskiǐ Yu.L. Itô equations and differential geometry.-Usp. matem. nauk, 1982, v. 37, No. 3 (in Russian).
Bismut J.-M. Mécanique Aléatoire. Lect. Notes in Math., 1981, v. 866.
Bishop R.L. and Crittenden R.J. Geometry of manifolds. Academic Press, N.Y.-London, 1964.
Vershik A.M. Classical and non-classical dynamics with constraints.-in: Geometry and topology in global non-linear problems (New problems in the global analysis), Voronezh, 1984 (in Russian) (English transl: Lect. Notes Math., v. 1108, 1984).
Gangolli R. On the construction of certain diffusions on a differentiable manifold.-Z. Wahrscheinlichkeitstheorie, 1964, Bd. 2.
Gikhman I.I. and Skorokhod A.V. Introduction to the theory of stochastic processes. Moscow, 1977 (in Russian).
Gikhman I.I. and Skorokhod A.V. The theory of stochastic processes. Moscow, 1975, v. 3 (in Russian).
Gliklikh Yu.E. Integral operators on a manifold.-Proc. Math. Dep. of Voronezh State University, Voronezh, 1971, No.4 (in Russian).
Gliklikh Yu.E. On a certain generalization of the Hopf-Rinow theorem about geodesics.-Usp. Matem. Nauk, 1974, v. 29, No. 6 (in Russian).
Gliklikh Yu.E. On non-local continuation conditions for integral curves of vector fields.-Dif. uravneniya, 1977, v.12, No. 4 (in Russian).
Gliklikh Yu.E. Riemannian parallel translation in non-linear mechanics.-in: Topological and geometrical methods in mathematical physics (New problems in the global analysis), Voronezh, 1983 (in Russian; English transl: Lect. Notes Math., v. 1108, 1984).
Gliklikh Yu.E. and Fedorenko I.V. On the geometrization of a certain class of mechanical systems with stochastic force perturbations.-Deposited at VINITI, October 1980, No. 4481-80 (in Russian).
Gliklikh Yu.E. and Fedorenko I.V. On the equations of geometrical mechanics with random force fields.-in: Approximate methods of studying differential equations and their applications, Kuibyshev, 1981 (in Russian).
Godbillon C. Géométrie différentielle et mécanique analytique. Hermann, Paris, 1969.
Daletskiǐ Yu.L. Stochastic differential geometry.-Usp. Matem. Nauk, 1983, v. 38, No. 3 (in Russian).
de Witt-Morett C. and Elworthy K.D. A stepping stone to stochastic analysis.-in: New stochastic methods in physics, Physics Reports, 1981, v. 77, No. 3.
Dombrowski P. On the geometry of the tangent bundle.-Journ. reine angew. Math., 1962, Bd. 210, Heft 1/2.
Eisenhart L.P. Riemannian geometry. Princeton University Press, 1926.
Eliasson H.I. Geometry of manifolds of maps.-J. Differential Geometry, 1967, v. 1, No. 2.
Elworthy K.D. Stochastic differential equations on manifolds. Cambridge, 1982 (London Mathematical Society Lecture Notes Series, v. 70).
Itô K. On stochastic differential equations on a differentiable manifold. 1.-Nagoya Math. J., 1950, v. 1, No. 1.
Itô K. Stochastic parallel displacement. Lect. Notes in Math., 1975, v. 451.
Kobayashi S. and Nomizu K. Foundations of differential geometry. Interscience, N.Y.-London, 1963.
Liptser R.Sh. and Shiryaev A.N. Statistics of stochastic processes. Moscow, 1974 (in Russian).
Malliavin P. Géométrie différentielle stochastique. Montréal, 1978.
Meyer P.A. A differential-geometric formalism for Itô calculus.-Lect. Notes in Math., 1981, v. 851.
Sternberg S. Lectures on differential geometry. Prentice Hall, N. J., 1964.
Synge J.L. Hodographs of general dynamical systems.-Trans. Roy. Soc. Canada, Ser. 3, 1926, vol. 25.
Gliklikh Yu.E. On Riemannian metrics possesing uniform Riemannian atlas.-Differential geometry of manifolds of figures, Kaliningrad Univ., 1985, No 16.
Gliklikh Yu.E. Curvilinear Itô integral with Riemannian parallel translation and stochastic equations on manifolds.-Theory of Probability and Mathematical Statistics, Kiev, 1986, No 35 (in Russian).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this chapter
Cite this chapter
Gliklikh, Y.E. (1986). Riemannian parallel translation, the ito integral, and stochastic equations on manifolds. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis — Studies and Applications II. Lecture Notes in Mathematics, vol 1214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075965
Download citation
DOI: https://doi.org/10.1007/BFb0075965
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16821-8
Online ISBN: 978-3-540-47084-7
eBook Packages: Springer Book Archive