Refinements in martingale analysis

  • M. M. Rao
Part of the Mathematics and Its Applications book series (MAIA, volume 342)


In order to obtain finer and specialized results from the basic theory of martingales, we introduce a new tool called the stopping time or optional transformation and investigate various properties of martingales under the effect of these mappings. A number of technical (measure theoretical) problems arise when such families are considered, and we present a detailed analysis of these processes together with their structure and limit theory. Both the directed and linearly ordered index sets of the (sub-) martingales are considered. A consequence here is the culmination of a proof of the existence of projective limits of certain systems and the associated class (D) martingales. The study leads to several decompositions of processes that are useful in applications.


Regularity Property Projective System Predictable Process Convergence Theory Martingale Difference 
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.


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© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • M. M. Rao
    • 1
  1. 1.University of CaliforniaRiversideUSA

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