Titlebook: Stochastic Calculus and Applications; Samuel N. Cohen,Robert J. Elliott Textbook 2015Latest edition Springer Science+Business Media New Yo

摘要

The Doob–Meyer Decompositionus uniformly integrable supermartingale . is said to be of class (D) if the set of random variables . is uniformly integrable (where . is the set of all stopping times). These were introduced in Section .

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Filtrations, Stopping Times and Stochastic Processesach of which is random. Our goal in this section is to build a mathematical understanding of these ‘stochastic processes’, that is, of collections of random variables, the values of which become revealed through time.

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反感

The Doob–Meyer Decompositionundamentally useful property, and in this chapter we show that a similar decomposition holds for all right-continuous local supermartingales (and hence local submartingales). To obtain this, we first consider the particularly ‘nice’ class of processes given by class (D). Recall that a right-continuo

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