2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75865We give two stochastic diffeologies on the free loop space which allow us to define stochastic equivariant cohomology theories in the Chen-Souriau sense and to establish a link with cyclic cohomology. With the second one, we can establish a stochastic fixed point theorem.Published at http://dx.doi.org/10.1214/009117905000000170 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability58J65, 55N91, 46L80 (Primary)text