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The characterization and understanding of online social network behavior isof importance from both the points of view of fundamental research andrealistic utilization. In this manuscript, we propose a stochastic differentialequation to describe the online microblogging behavior. Our analysis is basedon the microblog data collected from Sina Weibo which is one of the mostpopular microblogging platforms in China. Especially, we focus on thecollective nature of the microblogging behavior reflecting itself in theanalyzed data as the characters of the periodic pattern, the stochasticfluctuation around the baseline, and the extraordinary jumps. Compared withexisting works, we use in our model time dependent parameters to facilitate theperiodic feature of the microblogging behavior and incorporate a compoundPoisson process to describe the extraordinary spikes in the Sina Weibo volume.Such distinct merits lead to significant improvement in the predictionperformance, thus justifying the validity of our model. This work may offerpotential application in the future detection of the anomalous behavior inonline social network platforms.

Modeling Collective Behavior of Posting Microblog by Stochastic Differential Equation with Jump