Nonstationary optimal paths and tails of prehistory probability density in multistablestochastic systems

The tails of prehistory probability density in nonlinear multistable stochastic systems driven by white Gaussian noise, which has been a subject of recent study, are analyzed by employing the concepts of nonstationary optimal fluctuations. Results of numerical simulations show that the prehistory probability density is non-Gaussian and highly asymmetrical, and that it is an essential feature of noise driven fluctuations in nonlinear systems. We also show that in systems with detailed balance the prehistory probability density is the conventional transition probability that obeys the backward Kolmogorov equation.