Superdiffusive limits for deterministic fast–slow dynamical systems

We consider deterministic fast–slow dynamical systems on Rm× Y of the form {xk+1(n)=xk(n)+n-1a(xk(n))+n-1/αb(xk(n))v(yk),yk+1=f(yk),where α∈ (1 , 2). Under certain assumptions we prove convergence of the m-dimensional process Xn(t)=x⌊nt⌋(n) to the solution of the stochastic differential equation dX=a(X)dt+b(X)⋄dLα,where Lα is an α-stable Lévy process and ⋄ indicates that the stochastic integral is in the Marcus sense. In addition, we show that our assumptions are satisfied for intermittent maps f of Pomeau–Manneville type.