Aleksandar Mijatović, Andrey Pilipenko, Isao Sauzedde
This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an $α$-stable process.
This paper contains 7 sections, 10 theorems, 66 equations.
Theorem 1.1
Let $\beta\in(1-\alpha, \frac{1}{1+\alpha})$. Assume $f$ is a $\mathcal{C}^1$ function such that $(\ln(f))'(x)=O(1/x)$ and $f(x)=a x^\beta +o(x^{\beta-r})$, with $r=(\alpha+\beta-1)/\alpha$, as $x\to \infty$. If in addition eq:assumption holds, then, as $\lambda\to \infty$, and the convergence is in distribution in the space of càdlàg functions (endowed with the topology of local uniform converge
