Random perturbations Blow-up 6 Metastability 6 Chaotic systems 4 Explosions 4 External perturbations 4 Fidelity amplitude 4 Lyapunov decay 4 Quantum chaotic systems 4 Random dynamics 4 Semiclassical approaches 4 Semiclassical theories 4 Stochastic differential equations 4 Billiard systems 2 Domain of attraction 2 Invariant measure 2 Linear equations 2 Metastabilities 2 Partial differential equations 2 Random processes 2 Reaction diffusion equations 2 Stable equilibrium 2 Stochastic partial differential equation 2 Stochastic partial differential equations 2 Stochastic systems 2 Time averages 2 Uniform ergodicity 2