The Stochastic Process π

  • Alan Bain
  • Dan Crisan
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 60)


The principal aim of this chapter is to familiarize the reader with the fact that the conditional distribution of the signal can be viewed as a stochastic process with values in the space of probability measures. While it is true that this chapter sets the scene for the subsequent chapters, it can be skipped by those readers whose interests are biased towards the applied aspects of the subject. The gist of the chapter can be summarized by the following.


Probability Measure Weak Convergence Weak Topology Optional Projection Integrable Martingale 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Alan Bain
    • 1
  • Dan Crisan
    • 2
  1. 1.BNP Paribas 10 Harewood AvLondonUnited Kingdom
  2. 2.Department of MathematicsImperial College London 180 Queen’s GateLondonUnited Kingdom

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