  We propose a novel problem formulation of continuous-time information
propagation on heterogenous networks based on jump stochastic differential
equations (SDE). The structure of the network and activation rates between
nodes are naturally taken into account in the SDE system. This new formulation
allows for efficient and stable algorithm for many challenging information
propagation problems, including estimations of individual activation
probability and influence level, by solving the SDE numerically. To this end,
we develop an efficient numerical algorithm incorporating variance reduction;
furthermore, we provide theoretical bounds for its sample complexity. Moreover,
we show that the proposed jump SDE approach can be applied to a much larger
class of critical information propagation problems with more complicated
settings. Numerical experiments on a variety of synthetic and real-world
propagation networks show that the proposed method is more accurate and
efficient compared with the state-of-the-art methods.
