Nonlinear effect on the first passage time distribution

A statistical theory on the transient process in a multiplicative noise system is developed. The system is set to be below the critical point where the dynamic variable approaches zero under the influence of the multiplicative noise. It is numerically shown that the first passage time distribution exhibits a single peak structure, and that it has an exponential form for long first passage times. We derive approximate analytic expressions for the first passage time distributions, which are in fairly good agreement with numerical results, where particularly concerning in relation to the nonlinear fluctuation effects.