The problem of divergences associated with point particles in electrodynamics is overcome by associating an extreme probability density for their smallest radial extent. Infinite self-energies leading to an infinite displacement of spectral lines are thereby avoided. Dynamic equilibrium selects out a particular frequency rather than a sum over an infinite number leading to logarithmic divergences. Stochastic processes associated with the classical Bohr theory, together with his quantum conditions, are sufficient to derive the Lamb shift and the magnetic moment of electron spin caused by irregular circular fluctuations (Zitterbewegung) of an electron.