Summary: A class of functions \({\mathcal H}^{\mathcal F}_ n\) is chosen, which are boundary values of holomorphic functions. It is shown that if the potential \(V \in {\mathcal H}^{\mathcal F}_ n\) and the initial wave function \(\psi \in {\mathcal H}^{\mathcal F}_ n\), then the solution of the Schrödinger equation is \(\psi_ t \in {\mathcal H}^{\mathcal F}_ n\). The unitary evolution \(\psi \to \psi_ t\) can be expressed by an integral with respect to the Wiener measure. To each \(\psi_ t \in {\mathcal H}^{\mathcal F}_ n\) a complex Markov process \({\mathbf q}_ t\) fulfilling stochastic Hamilton equations is associated. The time evolution of \(\psi\) as well as multi-time correlation functions of arbitrary observables in quantum mechanics take the form of expectation values with respect to \({\mathbf q}_ t\). Some statistical and ergodic aspects of quantum mechanics resulting from the stochastic interpretation of Feynman’s sum over trajectories are discussed.