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

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 

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References

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    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
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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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