The motion of a particle acted on by the deterministic force vector b(x(t)) and perturbed by random forces of white noise type is considered. Such a particle will leave any bounded domain OMEGA in finite time. We consider the case where b is such tat the boundary consists of a trajectory or trajectories of the system dx/dt equals b(x(t)). Thus the cases of an unstable limit cycle and a center are considered. Expressions are derived for the mean first passage time to the boundary and the probability distribution of exit points on the boundary.
ASJC Scopus subject areas
- Applied Mathematics