On the Transfer of the Wiener Measure to the Set of Continuous Trajectories in the Heisenberg Group

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 H 3 (ℝ) is considered such that the trajectories of this process, in the stochastic sense, satisfy the horizontality conditions with r...

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Veröffentlicht in:	Russian journal of mathematical physics 2019-10, Vol.26 (4), p.454-469
1. Verfasser:	Mamon, S. V.
Format:	Artikel
Sprache:	eng
Schlagworte:	Lie groups Mathematical and Computational Physics Physics Physics and Astronomy Stochastic processes Theoretical Trajectories
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container_title	Russian journal of mathematical physics
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description	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 H 3 (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 H 3 (ℝ). The main result claims that the measure defined on the trajectories of this process is completely concentrated on the set C ([0, t ], H 3 (ℝ)) of continuous trajectories.
doi_str_mv	10.1134/S1061920819040046
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subjects	Lie groups Mathematical and Computational Physics Physics Physics and Astronomy Stochastic processes Theoretical Trajectories
title	On the Transfer of the Wiener Measure to the Set of Continuous Trajectories in the Heisenberg Group
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