  In the paper, a novel distributed stochastic approximation algorithm (DSAA)
is proposed to seek roots of the sum of local functions, each of which is
associated with an agent from the multiple agents connected in a network. At
any time, each agent updates its estimate for the root utilizing the
observation of its local function and the information derived from the
neighboring agents. The key difference of the proposed algorithm from the
existing ones consists in the expanding truncations (so it is called as
DSAAWET), by which the boundedness of the estimates can be guaranteed without
imposing the growth rate constraints on the local functions. The convergence of
the estimates generated by DSAAWET to a consensus set belonging to the root set
of the sum function is shown under weaker conditions on the local functions and
on the observation noise in comparison with the existing results. We illustrate
our approach by two applications, one from signal processing and the other one
from distributed optimization. Numerical simulation results are also included.
