Every Nonnegative Submartingale is the Absolute Value of a Martingale
Gilat, David
Ann. Probab., Tome 5 (1977) no. 6, p. 475-481 / Harvested from Project Euclid
It is shown that every nonnegative superfair process (in particular a nonnegative submartingale) is the absolute value of a symmetric fair process (martingale). Is every submartingale a convex function of a martingale? No. If however the adjective convex is omitted from the question, an affirmative answer is provided. Furthermore, transforming functions $\phi$, such that every superfair process (submartingale) is that $\phi$ of a fair process (martingale), are shown to exist. The results are extended to continuous-parameter submartingales with rightcontinuous sample functions.
Publié le : 1977-06-14
Classification:  Superfair process,  submartingale,  convex function,  regular conditional distribution,  strategy,  60G45
@article{1176995809,
     author = {Gilat, David},
     title = {Every Nonnegative Submartingale is the Absolute Value of a Martingale},
     journal = {Ann. Probab.},
     volume = {5},
     number = {6},
     year = {1977},
     pages = { 475-481},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995809}
}
Gilat, David. Every Nonnegative Submartingale is the Absolute Value of a Martingale. Ann. Probab., Tome 5 (1977) no. 6, pp.  475-481. http://gdmltest.u-ga.fr/item/1176995809/