I read in D. Sornette's Critical Phenomena in Natural Sciences about the Kesten Multiplicative process:
$X_{n+1} = a_n X_n + b_n$ where $a_n$ and $b_n$ are stochastic variables drawn from the pdfs $P_{a_n}(a_n)$ and $P_{b_n}(b_n)$.
Sornette writes: "the random multiplicative coefficients $a_n$ lead to non-trivial intermittent behavior for a large class of distributions for $a_n$...it provides a simple and general mechanism for generating power law distributions."
Is it possible to prove that the Kesten Process can be used to generate a power law distribution? Or, if I wanted to find the class of $a_n$ distributions that yeild power law behavior, are there methods other than experimentation of doing that? ${{}}$