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An approach was developed to describe the first passage time (FPT) inmultistep stochastic processes with discrete states governed by a masterequation (ME). The approach is an extension of the totally absorbing boundaryapproach given for calculation of FPT in one-step processes (Van Kampen 2007)to include multistep processes where jumps are not restricted to adjacentsites. In addition, a Fokker-Planck equation (FPE) was derived from themultistep ME, assuming the continuity of the state variable. The developedapproach and an FPE based approach (Gardiner 2004) were used to find the meanfirst passage time (MFPT) of the transition between the negative and positivestable macrostates of dust grain charge when the charging process was bistable.The dust was in a plasma and charged by collecting ions and electrons, andemitting secondary electrons. The MFPTs for the transitioning of grain chargefrom one macrostate to the other were calculated by the two approaches for arange of grain sizes. Both approaches produced very similar results for thesame grain except for when it was very small. The difference between MFPTs oftwo approaches for very small grains was attributed to the failure of thecharge continuity assumption in the FPE description. For a given grain, theMFPT for a transition from the negative macrostate to the positive one wassubstantially larger than that for a transition in a reverse order. Thenormalized MFPT for a transition from the positive to the negative macrostateshowed little sensitivity to the grain radius. For a reverse transition, withthe increase of the grain radius, it dropped first and then increased. Theprobability density function of FPT was substantially wider for a transitionfrom the positive to the negative macrostate, as compared to a reversetransition.

First passage time in multi-step stochastic processes with applications to dust charging