Kramers' rate for systems with multiplicative noise.

Kramers' rate for the passage of trajectories X(t) over an energy barrier due to thermal or other fluctuations is usually associated with additive noise. We present a generalization of Kramers' rate for systems with multiplicative noise. We show that the expression commonly used in the literature for multiplicative noise is not correct, and we present results of numerical integrations of the Langevin equation for dX(t)/dt evolving in a quartic bistable potential which corroborate our claim.