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Onsager-Machlup Functional for Uniformly Elliptic Time-Inhomogeneous Diffusion

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Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 2123)

Abstract

In this paper, we will compute the Onsager-Machlup functional of an inhomogeneous uniformly elliptic diffusion process. This functional is very similar to the corresponding functional for homogeneous diffusions; indeed, the only difference come from the infinitesimal variation of the volume. We will also use the Onsager-Machlup functional to study small ball probability for weighted sup-norm of some inhomogeneous diffusion.

Keywords

  • Inhomogeneous Diffusion
  • Small Ball Estimates
  • Fermi Coordinates
  • Ricci flow
  • Time-dependent Family

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. M. Capitaine, On the Onsager-Machlup functional for elliptic diffusion processes, in Séminaire de Probabilités, XXXIV. Lecture Notes in Mathematics, vol. 1729 (Springer, Berlin, 2000), pp. 313–328

    Google Scholar 

  2. A.K. Coulibaly-Pasquier, Brownian motion with respect to time-changing riemannian metrics, applications to Ricci flow. Ann. Inst. Henri Poincaré Probab. Stat. 47(2), 515–538 (2011)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. A.K. Coulibaly-Pasquier, Some stochastic process without birth, linked to the mean curvature flow. Ann. Probab. 39(4), 1305–1331 (2011)

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. K. Hara, Y. Takahashi, Lagrangian for pinned diffusion process, in Itô’s Stochastic Calculus and Probability Theory (Springer, Tokyo, 1996), pp. 117–128

    Google Scholar 

  5. N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes. North-Holland Mathematical Library, vol. 24, 2nd edn. (North-Holland, Amsterdam, 1989)

    Google Scholar 

  6. J. Lott, Optimal transport and Perelman’s reduced volume. arXiv:0804.0343v2

    Google Scholar 

  7. Y. Takahashi, S. Watanabe, The probability functionals (Onsager-Machlup functions) of diffusion processes, in Stochastic Integrals, (Proc. Sympos., Univ. Durham, Durham, 1980). Lecture Notes in Mathematics, vol. 851 (Springer, Berlin, 1981), pp. 433–463

    Google Scholar 

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Correspondence to Koléhè A. Coulibaly-Pasquier .

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Coulibaly-Pasquier, K.A. (2014). Onsager-Machlup Functional for Uniformly Elliptic Time-Inhomogeneous Diffusion. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLVI. Lecture Notes in Mathematics(), vol 2123. Springer, Cham. https://doi.org/10.1007/978-3-319-11970-0_5

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