  This paper studies distributed stochastic approximation algorithms based on
broadcast gossip on communication networks represented by digraphs. Weak
convergence of these algorithms is proved, and an associated ordinary
differential equation (ODE) is formulated connecting convergence points with
local objective functions and network properties. Using these results, a
methodology is proposed for network design, aimed at achieving the desired
asymptotic behavior at consensus. Convergence rate of the algorithm is also
analyzed and further improved using an attached stochastic differential
equation. Simulation results illustrate the theoretical concepts.
