  Using the framework of random walks in random scenery, Cohen and
Samorodnitsky (2006) introduced a family of symmetric $\alpha$-stable motions
called local time fractional stable motions. When $\alpha=2$, these processes
are precisely fractional Brownian motions with $1/2<H<1$. Motivated by random
walks in alternating scenery, we find a "complementary" family of symmetric
$\alpha$-stable motions which we call indicator fractional stable motions.
These processes are complementary to local time fractional stable motions in
that when $\alpha=2$, one gets fractional Brownian motions with $0<H<1/2$.
