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Ukrainian Mathematical Journal

, Volume 52, Issue 4, pp 616–623 | Cite as

Logarithmic derivatives of diffusion measures in a Hilbert space

  • V. G. Bondarenko
Brief communications
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Abstract

For the logarithmic derivative of transition probability of a diffusion process in a Hilbert space, we construct a sequence of vector fields on Riemannian n-dimensional manifolds that converge to this derivative.

Keywords

HILBERT Space Vector Field Riemannian Manifold Gaussian Measure Diffusion Measure 
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.

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References

  1. 1.
    Yu. L. Daletskii and S. V. Fomin, Measures and Diffusion Equations in Infinite-Dimensional Spaces [in Russian], Nauka. Moscow (1983).Google Scholar
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    Yu. L. Daletskii and Ya. I. Belopol’skaya, Stochastic Equations and Differential Geometry [in Russian] Vyshcha Shkola, Kiev 1989.Google Scholar
  3. 3.
    V. G. Bondarenko, “Diffusion sur variete de courbure non positive,” Comptes Rendus, 324, No. 10, 1099–1103 (1997).MATHMathSciNetGoogle Scholar
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    V. G. Bondarenko, “Estimates of the heat kernel on a manifold of nonpositive curvature,” Ukr. Mat. Zh., 50, No. 8, 1129–1136 (1998).MATHCrossRefMathSciNetGoogle Scholar
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    V. G. Bondarenko, “Covariant derivatives of Jacobi fields on a manifold of nonpositive curvature,” Ukr. Mat. Zh., No. 6. 755–764 (1998).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • V. G. Bondarenko
    • 1
  1. 1.Kiev Politechnic InstituteKiev

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