Stochastic kinetics under combined action of two noise sources

We are exploring two archetypal noise induced escape scenarios: escape from a finite interval and from the positive half-line under the action of the mixture of L\'evy and Gaussian white noises in the overdamped regime, for the random acceleration process and higher order processes. In the case of escape from finite intervals, mixture of noises can result in the change of value of the mean first passage time in comparison to the action of each noise separately. At the same time, for the random acceleration process on the (positive) half-line, over the wide range of parameters, the exponent characterizing the power-law decay of the survival probability is equal to the one characterizing the decay of the survival probability under action of the (pure) L\'evy noise. There is a transient region, width of which increases with stability index $\alpha$, when the exponent decreases from the one for L\'evy noise to the one corresponding to the Gaussian white noise driving.Comment: 10 pages, 8 figure