Theory of Martingales
Theory of Martingales by R. Sh. Liptser , A. N. Shiryayev
English | PDF | 1989 | 806 Pages | ISBN : 0792303954 | 42.6 MB
In our earlier monograph 1 "Statistics of random processes", published in 1974, the martingale theory has been represented presumably by the square integrable case. Correspondingly, stochastic integration theory has also been described for square integrable martingales only.
During the last decade it became clear that, though the case of square integrable martingales is rather important, it does not meet all demands of intrinsic developments of the martingale theory and its applications. It became apparent that the basic concepts of the martingale theory are the notions of a local martingale and a semimartingale - a stochastic process representable as the sum of a local martingale and a process of locally bounded variation. Stochastic integration theory has been developed first relative to local martingales and then to semimartingales. At the same time the very construction of the stochastic integral H • X ;: f H dX with resp..!..:t to a semimartingale X revealed the essence and importance of the predictability concept, and of predictability conditions imposed on an integrand process H.
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