The total variation of a simple, symmetric random walk with absorbing barrier at zero, is stochastically larger than the total variation of any other nonnegative, integer-valued supermartingale with the same initial position. This strengthens a result of David Freedman on the optimality of timid play for maximizing the time to bankruptcy in certain gambling situations.
Publié le : 1977-08-14
Classification:
Martingale,
variation,
simple random walk,
gambling theory,
dynamic programming,
timid play,
decision theory,
60G45,
62L99
@article{1176995764,
author = {Gilat, David and Sudderth, William},
title = {Timid Play when Large Bets are Profitable},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 573-576},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995764}
}
Gilat, David; Sudderth, William. Timid Play when Large Bets are Profitable. Ann. Probab., Tome 5 (1977) no. 6, pp. 573-576. http://gdmltest.u-ga.fr/item/1176995764/