Random attractor for stochastic lattice dynamical systems with α-stable Lévy noises

• We show that the stochastic lattice dynamical systems with α-stable Lévy noises generate a random dynamical system in ℓ2.
• Prove the existence of a unique random attractor for the random dynamical system.
• We provide some first steps for considering random attractors for stochastic lattice dynamical systems driven by Lévy noises.

The present paper is devoted to the existence of a random attractor for stochastic lattice dynamical systems with α-stable Lévy noises.