... 19 05 2014 The first-passage problem of quasi-nonintegrable Hamiltonian systems subject to light linear/nonlinear dampings and weak external/parametric random excitations is investigated here. The motivation is to acquire asymptotic analytical solution of the first-passage rate or the mean...

... the difficulty of the first-passage problem, since even in the simplest case of a linear oscillator under white noise excitation, an exact closed form solution for the survival probability has not been feasible so far. Clearly, Monte Carlo simulation (MCS)–based approaches are among the most potent tools...