  It was recently realized that the persistence exponent appearing in the
dynamics of nonequilibrium systems is a special member of a continuously
varying family of exponents, describing generalized persistence properties. We
propose and solve a simplified model of coarsening, where time intervals
between spin flips are independent, and distributed according to a L\'evy law.
Both the limit distribution of the mean magnetization and the generalized
persistence exponents are obtained exactly.
