A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations

Solutions to the Schrödinger, heat and stochastic Schrödinger equation with rather general potentials are represented, both in __x__- and __p__-representations, as integrals over the path space with respect to σ-finite measures. In the case of __x__-representation, the corresponding measure is concentrated on the Cameron–Martin Hilbert space of curves with __L__^2^-integrable derivatives. The case of the Schrödinger equation is treated by means of a regularization based on the introduction of either complex times or continuous non-demolition observations.