THE PERTURBATION APPROXIMATION OF THE MEAN FIRST-PASSAGE TIME FOR NONLINEAR NON-MARKOVIAN CONTINUOUS-PROCESSES

In this paper, we generalize the method which is presented by J. Masol iver [J. Masoliver, Phys. Rev. A45 (1992) 2256] to calculate the mean first-passage time (MFPT) for the systems driven by nonlinear non-Mark ovian continuous noises. We present the perturbation approximation met hod for treating the near-free systems and the ones that can be transf ormed into near-free systems, and we give the general calculation form ula for the zero-order and first-order approximations of the MFPT. We apply the method to three typical examples with rectangular temporal d istribution in detail. The first is about the nonlinear free process; the second is about the stochastic process with square nonlinear drift ; the third is about the stochastic process driven by multiplicative a nd additive noises altogether.