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.

中文翻译：

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海森堡群中维纳测度向连续轨迹集的转移

在本文中，研究了关于零幂李群上的随机过程理论的问题。特别地，考虑了海森堡群H ₃（ℝ）上的随机过程，使得该过程的轨迹在随机意义上满足关于H ₃（ℝ）上的标准接触结构的水平条件。主要结果声称，在此过程的轨迹上定义的测度完全集中在连续轨迹的集合C（[0，t ]，H ₃（ℝ））上。