Communications in Mathematical Sciences

Volume 18 (2020)

Number 8

A jump stochastic differential equation approach for influence prediction on heterogenous networks

Pages: 2341 – 2359



Yaohua Zang (School of Mathematics, Zhejiang University, Zhejiang, Hangzhou, China)

Gang Bao (School of Mathematics, Zhejiang University, Zhejiang, Hangzhou, China)

Xiaojing Ye (Department of Mathematics and Statistics, Georgia State University, Atlanta, Ga., U.S.A.)

Hongyuan Zha (School of Data Science, Shenzhen Research Institute of Big Data, Chinese University of Hong Kong, Shenzhen, China)

Haomin Zhou (School of Mathematics, Georgia Institute of Technology, Atlanta, Ga., U.S.A.)


We propose a novel problem formulation of continuous-time information propagation on heterogeneous networks based on jump stochastic differential equations (JSDE). The structure of the network and activation rates between nodes are naturally taken into account in the JSDE. This new formulation allows for efficient and stable algorithms for a variety of challenging information propagation problems, including estimations of individual activation probability and influence level, by solving the JSDE numerically. In particular, we develop an efficient numerical algorithm for solving the JSDE by incorporating variance reduction; and furthermore, we provide theoretical bounds for its sample complexity. Numerical experiments on a variety of propagation networks show that the proposed method is more accurate and efficient compared with the state-of-the-art methods, and more importantly it can be applied to solve other critical information propagation problems to which existing methods cannot be applied.


propagation network, stochastic differential equation with jump, heterogeneous network, influence prediction, complexity

2010 Mathematics Subject Classification

65Y10, 90B18, 94A20

G. Bao and Y. Zang are supported in part by NSFC Innovative Group Fund (No.11621101). X. Ye is supported in part by NSF DMS-1620342, CMMI-1745382, DMS-1818886 and DMS-1925263. H. Zha is supported in part by NSFC Grant No. 61672231 and Grant No. U16092202, as well as Shenzhen Research Institute for Big Data. H. Zhou is supported in part by NSF DMS-1620345 and DMS-1830225, and ONR N00014- 18-1-2852.

Received 3 July 2019

Accepted 10 July 2020

Published 22 December 2020