Example of a non-Gaussian n-point bifurcation for stochastic Lévy flows

We explore the elementary observation that a Markov chain with values in a finite space $M$ with $|M| = m$, $m\geq 2$, has many different extensions to a compatible $n$-point Markov chain in $M^n$, for all $1< n\leq m$. Embedding this phenomenon into the context of stochastic L\'evy flows of diffeomorphisms in Euclidean spaces, we introduce the notion of an $n$-point bifurcation of a stochastic flow. Roughly speaking a $n$-point bifurcation takes place, when a small perturbation of the stochastic flow does not change the characteristics at lower level $k$-point motions, $k