This chapter gives a survey of the theory of square-integrable martingales and the construction of basic sets of orthogonal martingales in terms of which all other martingales may be expressed as stochastic integrals. Specific cases such as Brownian motion, Lévy processes and stochastic jump processes are discussed, as are some applications to mathematical finance.
CITATION STYLE
Davis, M. H. A. (2005). Martingale representation and all that. In Systems and Control: Foundations and Applications (pp. 57–68). Birkhauser. https://doi.org/10.1007/0-8176-4409-1_4
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