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Parallel transports associated to stochastic holonomies

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Abstract

A stochastic holonomy along a loop obtained from the OU process on the path space over a compact Riemannian manifold is computed. The result shows that the stochastic holonomy just gives the parallel transport with respect to the Markov connection along the OU process on the path space

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Chen Shiping

  2. Zhuzhou Institute of Technology, Zhuzhou, 412008, China

    Chen Shiping

  3. Department of Mathematics, Hunan Normal University, 410081, Changsha, China

    Xiang Kainan

Authors
  1. Chen Shiping
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  2. Xiang Kainan
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Correspondence to Chen Shiping.

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Shiping, C., Kainan, X. Parallel transports associated to stochastic holonomies. Sci. China Ser. A-Math. 45, 1567–1577 (2002). https://doi.org/10.1360/02ys9168

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  • DOI: https://doi.org/10.1360/02ys9168

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