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Stochastic Processes: General Theory pp 233–331Cite as

Refinements in martingale analysis

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 342))

Abstract

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.

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Rao, M.M. (1995). Refinements in martingale analysis. In: Stochastic Processes: General Theory. Mathematics and Its Applications, vol 342. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6598-4_4

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