  We prove the existence of multiple noise-induced transitions in the
Lasota-Mackey mapl, which is a class of one-dimensional random dynamical system
with additive noise. The result is achieved by rigorous computer assisted
estimates. We first approximate the stationary distribution of the random
dynamical system and then compute certifiederror intervals for the Lyapunov
exponent. We find that the signs of the Lyapunov exponents changes at least
three times when increasing the noise amplitude. We also show numerical
evidence that the standard non-rigorous numericalapproximation by finite-time
Lyapunov exponents is valid with our model for a sufficiently large number of
iterations.Our method is expected to work for a broad class of nonlinear
stochastic p
