  The characterization and understanding of online social network behavior is
of importance from both the points of view of fundamental research and
realistic utilization. In this manuscript, we propose a stochastic differential
equation to describe the online microblogging behavior. Our analysis is based
on the microblog data collected from Sina Weibo which is one of the most
popular microblogging platforms in China. Especially, we focus on the
collective nature of the microblogging behavior reflecting itself in the
analyzed data as the characters of the periodic pattern, the stochastic
fluctuation around the baseline, and the extraordinary jumps. Compared with
existing works, we use in our model time dependent parameters to facilitate the
periodic feature of the microblogging behavior and incorporate a compound
Poisson process to describe the extraordinary spikes in the Sina Weibo volume.
Such distinct merits lead to significant improvement in the prediction
performance, thus justifying the validity of our model. This work may offer
potential application in the future detection of the anomalous behavior in
online social network platforms.
