The purpose of this chapter is to describe and investigate the main features of stochastic analysis on smooth manifolds. Our principal focus shall be on stochastic differential equations. A monographic presentation of various alternative aspects of and approaches to stochastic analysis on manifolds can be found in (Belopolskaya and Dalecky, 1989), (Elworthy, 1982), (Emery, 1989), (Hsu, 2002), Meyer (Lecture Notes in Mathematics 850, 1981; Lecture Notes in Mathematics 851, 1981), (Nelson, 1985), (Schwartz, 1984).


Weak Solution Riemannian Manifold Tangent Space Strong Solution Wiener Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 23.
    Belopolskaya, Ya.I., Dalecky, Yu.L.: Stochastic processes and differential geometry. Kluwer Academic Publishers, Dordrecht (1989) Google Scholar
  2. 66.
    Elworthy, K.D.: Stochastic differential equations on manifolds. / Lect. Notes of London Math. Soc. 70. Cambridge University Press, Cambridge (1982) MATHGoogle Scholar
  3. 69.
    Emery, M.: Stochastic calculus on manifolds. Springer, Berlin et al. (1989) Google Scholar
  4. 147.
    Hsu, E.P.: Stochastic Analysis on Manifolds (Graduate Studies in Mathematics, Volume 38). AMS, Providens, R.I. (2002) MATHGoogle Scholar
  5. 179.
    Meyer, P.A.: Géométrie stochastique sans larmes. Lecture Notes in Mathematics. 850, 44-102 (1981) CrossRefGoogle Scholar
  6. 180.
    Meyer, P.A.: A differential geometric formalism for the Itô calculus. Lecture Notes in Mathematics. 851, 256-270 (1981) CrossRefGoogle Scholar
  7. 190.
    Nelson, E.: Quantum fluctuations. Princeton University Press, Princeton (1985) MATHGoogle Scholar
  8. 205.
    Schwartz, L.: Semimartingales and their stochastic calculus on manifolds. Montreal University Press, Montreal (1984) MATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentVoronezh State UniversityVoronezhRussia

Personalised recommendations