Limit theorems on the exit problems for small random perturbations of dynamical systems II

抄録

We consider small random perturbations of dynamical systems {u^ε(t)}_0{≤}t (0<ε) on C(S¹; R) when unperturbed dynamical systems {u^ε(t)}_0{≤}t have the only one asymptotically stable equilibrium point g₀(∈C(S¹; R)). The objects under consideration are empirical measures which are marginal measures of empirical processes at the exit time τ_D^ε of {u^ε(t)}_0{≤}t from a bounded domain D(∋g₀) of C(S¹; R), {u^ε(t)}_{0{≤}t{≤}τD^ε} and {u^ε(τ_D^εt)}_{0{≤}t{≤}1}.