Martingale Representation and All That [chapter]

Mark H. A. Davis
Systems and Control: Foundations & Applications  
This paper 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.
doi:10.1007/0-8176-4409-1_4 fatcat:m5kjyxevsndyvpv2g52bqnu4my