Nelsonian mechanics revisited

In de Broglie and Bohm's pilot-wave theory, as is well known, it is possibl e to consider alternative particle dynamics while still preserving the \psi \(2) distribution. I present the analogous result for Nelson's stochastic t heory, thus characterising the most general diffusion processes that preser ve the quantum equilibrium distribution, and discuss the analogy with the c onstruction of the dynamics for Bell's beable theories. I briefly comment o n the problem of convergence to \psi\(2) and on possible experimental const raints on the alternative dynamics.