Propagation of Chaos
This chapter is concerned with propagation-of-chaos properties of particle models. These properties measure the adequacy of the laws of the particles with the desired limiting distribution. They also allows us to quantify the independence between particles. Loosely speaking, the initial configuration of an N-particle model consists of N independent particles in a “complete chaos.” Then they evolve and interact with one another. The nature of the interactions depends on the McKean interpretation of the limiting process (see Section 2.5.3). For any fixed time horizon n, when the size of the system N, tends to infinity, any finite block of q(≤ N) particles asymptotically behaves as a collection of independent particles. In other words, the law of any q particle paths of length n converges as N → ∞ towards the q tensor product of the n-path McKean measure.
KeywordsRelative Entropy Particle Model Path Space Markov Transition Interact Particle System
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