Estimates Uniform in Time for the Transition Probability of Diffusions with Small Drift and for Stochastically Perturbed Newton Equations

Sergio Albeverio, Astrid Hilbert and Vassili Kolokoltsov
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Sergio Albeverio: Ruhr-Universität
Astrid Hilbert: Ruhr-Universität
Vassili Kolokoltsov: Ruhr-Universität

Journal of Theoretical Probability, 1999, vol. 12, issue 2, 293-300

Abstract: 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.

Keywords: Diffusion processes; transition probability; Newton's law (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021665708716

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