Narrow Results

We consider families of life distributions with the first three moments belonging to small neighborhoods of respective powers of a positive number. For various shapes of the neighborhoods, we determine exact convergence rates of their Prokhorov radii to zero. This provides a refined evaluation of the effect of specific moment convergence on the weak one.

We study the joint linear complexity of linear recurring multisequences, i.e., of multisequences consisting of linear recurring sequences. The expectation and variance of the joint linear complexity of random linear recurring multisequences are determined. These results extend the corresponding results on the expectation and variance of the joint linear complexity of random periodic multisequences. Then we enumerate the linear recurring multisequences with fixed joint linear complexity and determine the generating polynomial for the distribution of joint linear complexities. The proofs use new methods that enable us to obtain results of great generality.