Seminar Event Detail

Financial/Actuarial Mathematics

Date:  Wednesday, January 08, 2020
Location:  1360 East Hall (4:00 PM to 5:00 PM)

Title:  Mean field interaction on random graphs with dynamically changing multi-color edges

Abstract:   We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution of all other nodes and the corresponding edges, while the edge dynamics depends on the corresponding nodes. Asymptotic results, including law of large numbers, propagation of chaos, and central limit theorems, are established. In contrast to the classic McKean-Vlasov limit, the limiting system exhibits a path-dependent feature in that the evolution of a given particle depends on its own conditional distribution given its past trajectory. We also analyze the asymptotic behavior of the system when the edge dynamics is accelerated. A law of large number and a propagation of chaos result is established, and the limiting system is given as independent McKean-Vlasov processes. Errors between the two limiting systems, with and without acceleration in edge dynamics, are also analyzed.

Joint work with Erhan Bayraktar


Speaker:  Ruoyu Wu
Institution:  UM

Event Organizer:     


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