In this section we briefly describe some preliminary facts about mean derivatives. For details, see (Azarina and Gliklikh, 2007), (Gliklikh, 1996, 1997, 2005), (Nelson, 1967, 1985). This notion was first introduced by E. Nelson (1966, 1967, 1985) for the needs of so-called stochastic mechanics (see Chapter 15) but it turns out to be useful in some other problems of mathematical physics, economics, and elsewhere.


Weak Solution Linear Space Probability Space Conditional Expectation Wiener Process 


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  1. 7.
    Azarina, S.V., Gliklikh, Yu.E.: Differential inclusions with mean derivatives. Dynamic Systems and Applications. 16 (1), 49-71 (2007) MATHMathSciNetGoogle Scholar
  2. 106.
    Gliklikh, Yu.E.: Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics. Kluwer, Dordrecht (1996) MATHGoogle Scholar
  3. 107.
    Gliklikh, Yu.E.: Global Analysis in Mathematical Physics. Geometric and Stochastic Methods. Springer-Verlag, New York (1997) MATHGoogle Scholar
  4. 115.
    Gliklikh, Yu.E.: Global and stochastic analysis in problems of mathematical physics. KomKniga, Moscow (2005) (Russian) Google Scholar
  5. 187.
    Nelson, E.: Derivation of the Schrödinger equation from Newtonian mechanics. Phys. Reviews. 150 (4), 1079-1085 (1966) CrossRefGoogle Scholar
  6. 188.
    Nelson, E.: Dynamical theory of Brownian motion. Princeton University Press, Princeton (1967) Google Scholar
  7. 190.
    Nelson, E.: Quantum fluctuations. Princeton University Press, Princeton (1985) MATHGoogle Scholar

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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentVoronezh State UniversityVoronezhRussia

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