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.
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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
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)
A.K. Coulibaly-Pasquier, Some stochastic process without birth, linked to the mean curvature flow. Ann. Probab. 39(4), 1305–1331 (2011)
K. Hara, Y. Takahashi, Lagrangian for pinned diffusion process, in Itô’s Stochastic Calculus and Probability Theory (Springer, Tokyo, 1996), pp. 117–128
N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes. North-Holland Mathematical Library, vol. 24, 2nd edn. (North-Holland, Amsterdam, 1989)
J. Lott, Optimal transport and Perelman’s reduced volume. arXiv:0804.0343v2
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
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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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DOI: https://doi.org/10.1007/978-3-319-11970-0_5
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