Abstract
In the paper, problems related to the theory of stochastic processes on nilpotent Lie groups are studied. In particular, a stochastic process on the Heisenberg group H3(ℝ) is considered such that the trajectories of this process, in the stochastic sense, satisfy the horizontality conditions with respect to the standard contact structure on H3(ℝ). The main result claims that the measure defined on the trajectories of this process is completely concentrated on the set C([0, t], H3(ℝ)) of continuous trajectories.
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Acknowledgment
The author expresses his great gratitude to research supervisor E. T. Shavgulidze for setting the problem and valuable comments in the preparation of the text of the paper.
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Mamon, S.V. On the Transfer of the Wiener Measure to the Set of Continuous Trajectories in the Heisenberg Group. Russ. J. Math. Phys. 26, 454–469 (2019). https://doi.org/10.1134/S1061920819040046
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DOI: https://doi.org/10.1134/S1061920819040046