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The generalised Langevin equation with a retarded friction and a double-wellpotential is solved. The random force is modelled by a multiplicative noisewith long jumps. Probability density distributions converge with time to adistribution similar to a Gaussian but tails have a power-law form. Dependenceof the mean first passage time on model parameters is discussed. Properties ofthe stochastic resonance, emerging as a peak in the plot of the spectralamplification against the temperature, are discussed for various sets of themodel parameters. The amplification rises with the memory and is largest forthe cases corresponding to the large passage time.

Bistable generalised Langevin dynamics driven by correlated noise possessing a long jump distribution: barrier crossing and stochastic resonance