Abstract
An estimate uniform in time for the transition probability of diffusion processes with small drift is given. This also covers the case of a degenerate diffusion describing a stochastic perturbation of a particle moving according to the Newton's law. Moreover the random wave operator for such a particle is described and the analogue of asymptotic completeness is proven, the latter in the case of a sufficiently small drift.
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Albeverio, S., Hilbert, A. & Kolokoltsov, V. Estimates Uniform in Time for the Transition Probability of Diffusions with Small Drift and for Stochastically Perturbed Newton Equations. Journal of Theoretical Probability 12, 293–300 (1999). https://doi.org/10.1023/A:1021665708716
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DOI: https://doi.org/10.1023/A:1021665708716