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We prove the existence of multiple noise-induced transitions in theLasota-Mackey map, which is a class of one dimensional random dynamical systemwith additive noise. The result is achieved by the help of rigorous computerassisted estimates. We first approximate the stationary distribution of therandom dynamical system and then compute certified error intervals for theLyapunov exponent. We find that the sign of the Lyapunov exponent changes atleast three times when increasing the noise amplitude. We also show numericalevidence that the standard non-rigorous numerical approximation by finite-timeLyapunov exponent is valid with our model for a sufficiently large number ofiterations. Our method is expected to work for a broad class of nonlinearstochastic phenomena.

Existence of multiple noise-induced transitions in a Lasota-Mackey map