Some results on the problem of exit from a domain

The problem of exit from a domain of attraction of a stable equilibrium point in the presence of small noise is considered for a class of two-dimensional systems. It is shown that for these systems, the exit measure is 'skewed' in the sense that if S denotes the saddle point in the quasipotential towards which the exit measure collapses as the noise intensity goes to zero, then there exists an ε dependent neighborhood Δ of S such that lim P(exit in Δ)/{divides}Δ{divides}=0. Thus, the most probable exit point is not S but is rather skewed aside by ε^γ for some γ. The behaviour of such skewness, which was predicted by asymptotic expansions, depends on the ratio of normal to tangential forces around the saddle point.