Sharp Bounds for the Total Variance of Uniformly Bounded Semimartingales

Dubins, Lester E.

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 1559-1565 / Harvested from Project Euclid

Résumé

Let $S_n = f + X_1 + \cdots + X_n$ be an expectation-decreasing semimartingale with values in the unit interval, and let $V_n$ be the conditional variance of $X_n$ given the past. Then $E(\sum V_n)$ is less than $f(2 - f)$, and this bound is sharp. Sharper bounds are available if the process $S_0, S_1, \cdots$ satisfies suitable additional constraints.

Publié le : 1972-10-14
Classification:

@article{1177692388,
     author = {Dubins, Lester E.},
     title = {Sharp Bounds for the Total Variance of Uniformly Bounded Semimartingales},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 1559-1565},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692388}
}

Dubins, Lester E. Sharp Bounds for the Total Variance of Uniformly Bounded Semimartingales. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  1559-1565. http://gdmltest.u-ga.fr/item/1177692388/