Abstract
We prove the transportation inequality with the uniform norm for the laws of diffusion processes with Lipschitz and/or dissipative coefficients and apply them to some singular stochastic differential equations of interest.
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References
Cépa, E.: Equations différentielles stochastiques multivoques. Séminaire de Probabilités, tome 29, pp. 86–107. Lecture Notes in Math., vol. 1613 (1995)
Cépa, E., Lepingle, D.: Diffusing particles with electrostatic repulsion. Probab. Theor. Relat. Fields 107, 429–449 (1992)
Cépa, E., Lepingle, D.: Brownian particles with electrostatic repulsion on the circle: Dyson’s model for unitary random matrices revisited. ESAIM: Probab. Stat. 5, 203–224 (2001)
Djellout, H., Guillin, A., Wu, L.: Transportation cost-information inequalities and applications to random dynamical systems and diffusions. Ann. Probab. 32, 2702–2732 (2004)
Feyel, D., Üstünel, A.S.: Measure transport on Wiener space and the Girsanov Theorem. C.R. Acad. Sci. Paris, Ser. I, 1025–1028 (2002)
Feyel, D., Üstünel, A.S.: Monge–Kantorovitch measure transportation and Monge-Ampère equation on Wiener space. Probab. Theor. Relat. Fields 128(3), 347–385 (2004)
Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North Holland, Amsterdam (Kodansha Ltd., Tokyo) (1981)
Pal, S.: Concentration for multidimensional diffusions and their boundary local times. arXiv: 1005.2217v2 [math.PR], June 2010
Rogers, L.C.G., Williams, D.: Diffusions, Markov Processes, and Martingales, vol. 2, Itô Calculus. Wiley, New York (1987)
Talagrand, M.: Transportation cost for Gaussian and other product measures. Geom. Funct. Anal. 6, 587–600 (1996)
Villani, C.: Topics in Optimal Transportation. American Mathematical Society, Providence (2003)
Wu, L., Zhang, Z.L.: Talagrand’s T 2-transportation inequality w. r. to a uniform metric for diffusions. Acta Math. Appl. Sinica, English Series 20(3), 357–364 (2004)
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Üstünel, A.S. (2012). Transportation Cost Inequalities for Diffusions Under Uniform Distance. In: Decreusefond, L., Najim, J. (eds) Stochastic Analysis and Related Topics. Springer Proceedings in Mathematics & Statistics, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29982-7_9
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DOI: https://doi.org/10.1007/978-3-642-29982-7_9
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