Integral Representation of Martingales

Part of the Indian Statistical Institute Series book series (INSIS)


In this chapter we will consider the question as to when do all martingales adapted to a filtration \(({\mathcal F}_\centerdot )\) admit a representation as a stochastic integral with respect to a given local martingale M. This result was proved by Ito’s when the underlying filtration is the filtration generated by a multidimensional Wiener process. Ito’s had proven the integral representation property for square integrable martingales and this was extended to all martingales by Clark.

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Chennai Mathematical InstituteSiruseriIndia

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