This volume contains two papers:

The first paper (by Courrege and Renouard) is a mainly self-contained and detailed explication of the links between the corresponding interaction equations of the Quantum and Euclidian fields... in the so called trivial case when the space time dimen­ sion d is one. The key objects are the quasi-invariant measures on $\mathbb{R}$ and $C(\mathbb{R}, \mathbb{R})$ associated respectively to the Quantum field and to the Euclidian field ; the emphasis is laid on the deter­ mination of the fields directly from the interaction equations rather than by perturbation of the free ones ; and the involved techniques are those of functionnal analysis in Hilbert space.

The second paper (by Priouret and Yor) is a direct stu­ dyofthequasi-invariant Euclidian measure on $C(\mathbb{R}, \mathbb{R})$ from
the point of view and by the techniques of diffusion processes theory.