Abstract
In this paper, we study the distorted Ornstein-Uhlenbeck processes associated with given densities on an abstract Wiener space. We prove that the laws of distorted Ornstein-Uhlenbeck processes converge in total variation norm if the densities converge in Sobolev space \( D^{1}_{2} \).
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Albeverio, S., Röckner, M., Zhang, T.S. Girsanov transform for symmetric diffusions with infinite dimensional state space. The Annals of Probability, 21(2): 961–978 (1993)
Dell’Antonio, G.F., Posilicano, A. Convergence of Nelson Diffusions. Commun. Math. Phys., 141: 559–576 (1991)
Fukushima, M., Oshima, Y., Takeda, M. Dirichlet forms and symmetric Markov processes. Walter de Gruyter, Berlin, New York, 1994
Lyons, T.J., Zhang, T.S. Decomposition of Dirichlet processes and its applications. The Annals of Probability, 22(1): 494–524 (1994)
Posilicano, A. Convergence of distorted Brownian motions and singular Hamiltonians. Potential Analysis, 5: 241–271 (1996)
Röckner, M., Zhang, T.S. Uniqueness of generalized Schrödinger operators and applications. Journal of Functional Analysis, 105: 187–231 (1992)
Röckner, M., Zhang, T.S. Uniqueness of generalized Schrödinger operators, Part II. Journal of Functional Analysis, 119: 455–467 (1994)
Stroock, D.W., Varadhan, S.R.S. Multidimensional diffusion processes. Springer-Verlag, Berlin, Heidelberg, New York, 1979
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Posilicano, A., Zhang, T.S. Convergence of Symmetric Diffusions on Wiener Spaces. Acta Mathematicae Applicatae Sinica, English Series 20, 19–24 (2004). https://doi.org/10.1007/s10255-004-0144-4
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DOI: https://doi.org/10.1007/s10255-004-0144-4