Renormalization of Interacting Diffusions: A Program and Four Examples

2006 ◽  
pp. 123-136 ◽  
Author(s):  
F. den Hollander
Keyword(s):  
Interacting Diffusions

scholarly journals On the effect of heterogeneity on flocking behavior and systemic risk

2017 ◽  
Vol 34 (3-4) ◽  
Author(s):  
Fei Fang ◽  
Yiwei Sun ◽  
Konstantinos Spiliopoulos
Keyword(s):  
Asymptotic Formula ◽  
Case Studies ◽  
Systemic Risk ◽  
Mean Field ◽  
Loss Probability ◽  
Loss Distribution ◽  
Interacting Diffusions ◽  
The Mean ◽  
Laplace Asymptotics ◽  
Flocking Behavior

AbstractThe goal of this paper is to study organized flocking behavior and systemic risk in heterogeneous mean-field interacting diffusions. We illustrate in a number of case studies the effect of heterogeneity in the behavior of systemic risk in the system, i.e., the risk that several agents default simultaneously as a result of interconnections. We also investigate the effect of heterogeneity on the “flocking behavior” of different agents, i.e., when agents with different dynamics end up following very similar paths and follow closely the mean behavior of the system. Using Laplace asymptotics, we derive an asymptotic formula for the tail of the loss distribution as the number of agents grows to infinity. This characterizes the tail of the loss distribution and the effect of the heterogeneity of the network on the tail loss probability.

Comparison of interacting diffusions and an application to their ergodic theory

1996 ◽  
Vol 105 (4) ◽  
pp. 513-528 ◽  
Author(s):  
J. Theodore Cox ◽  
Klaus Fleischmann ◽  
Andreas Greven
Keyword(s):  
Ergodic Theory ◽  
Interacting Diffusions
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