Abstract: 

We construct fine mesh limits of vertex reinforced and vertex diminished jump processes on the line. Le limits are continuous stochastic processes on R with self-interaction and can be described using Bass-Burdzy stochastic flows. The continuous reinforced process has also a description as a mixture of Markovian diffusions in random potential. The continuous self-repelling process is related to the Ray-Knight identity for the 1D Bronwian motion. This is joint work with Christophe Sabot and Pierre Tarrès.