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We consider motion of a particle in a one-dimensional tilted ratchetpotential subject to two-sided tempered stable L\'{e}vy noise characterised bystrength $\Omega$, fractional index $\alpha$, skew $\theta$ and tempering$\lambda$. We derive analytic solutions to the corresponding Fokker-PlanckL\'{e}vy equations for the probability density. Due to the periodicity of thepotential, we carry out reduction to a compact domain and solve for theanalogue there of steady-state solutions which we represent as wrappedprobability density functions. By solving for the expected value of the currentassociated with the particle motion, we are able to determine threshold formetastability of the system, namely when the particle stabilises in a well ofthe potential and when the particle is in motion, for example as a consequenceof the tilt of the potential. Because the noise may be asymmetric, we examinethe relationship between skew of the noise and the tilt of the potential. Withtempering, we find two remarkable regimes where the current may be reversed ina direction opposite to the tilt or where the particle may be stabilised in awell in circumstances where deterministically it should flow with the tilt.

Noise driven current reversal and stabilisation in the tilted ratchet potential subject to tempered stable L\'{e}vy noise