Collective aggregation of a linearly coupled stochastic Cucker–Smale ensemble on asymmetric networks - Bae, Hyeong Ohk; Ha, Seung Yeal; Kim, Doheon; Kim, Yongsik; Lim, Hyuncheul; Yoo, Jane (Mathematical Methods in the Applied Sciences, 2021)
We study the stochastic aggregation of linearly coupled Cucker–Smale (CS) particles on several asymmetric networks. Our proposed first-order stochastic CS model was motivated as a stochastic dynamics modeling on the rates of multiasset return. In this study, we consider three asymmetric networks and study sufficient conditions toward stochastic aggregation for each proposed network. We also provide several numerical and empirical examples and compare them with theoretical results. In financial applications, we regard particles or agents as analysts and study their herding behavior based on our proposed model.
Keywords: Asymmetric networks; Cs models; Financial applications; First order; Herding behaviors; Stochastic aggregation; Stochastic dynamics models; aggregation; asymmetric networks; consensus; Cucker–Smale particles