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 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.