Advertisement

Propagation of Chaos

  • Pierre Del Moral
Part of the Probability and its Applications book series (PIA)

Abstract

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.

Keywords

Relative Entropy Particle Model Path Space Markov Transition Interact Particle System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York, LLC 2004

Authors and Affiliations

  • Pierre Del Moral
    • 1
  1. 1.Laboratoire de Statistique et ProbabilitésUniversité Paul SabatierToulouse, Cedex 4France

Personalised recommendations