Probability Evolution and Mean First-Passage Time for Multidimensional Non-Markovian Processes

We investigate a multidimensional system described by a set of stochastic differential equations in which the multiplicative noise is assumed to be an O-U noise. With the help of the projection operator technique, we derive an integrodifferential equation for the probability density and an approximate equation for the mean first-passage time (MFPT).Under some approximation, we obtain an effective Fokker-Planck equation and apply the equation to the single mode laser problem. The concrete calculations of MFPT are made with an important example.