Difference prophet inequalities for 
 [0,1]
-valued i.i.d. random variables with cost for observations

Kösters, Holger

Difference prophet inequalities for [0,1] -valued i.i.d. random variables with cost for observations

Ann. Probab., Tome 32 (2004) no. 1A, p. 3324-3332 / Harvested from Project Euclid

Résumé

Let X₁,X₂,… be a sequence of [0,1]-valued i.i.d. random variables, let c≥0 be a sampling cost for each observation and let Y_i=X_i−ic, i=1,2,…. For n=1,2,…, let M(Y₁,…,Y_n)=E(max _1≤i≤nY_i) and V(Y₁,…,Y_n)=sup _τ∈CⁿE(Y_τ), where Cⁿ denotes the set of all stopping rules for Y₁,…,Y_n. Sharp upper bounds for the difference M(Y₁,…,Y_n)−V(Y₁,…,Y_n) are given under various restrictions on c and n.

Publié le : 2004-10-14
Classification: Prophet inequality, optimal stopping, 60G40, 60E15

@article{1107883355,
     author = {K\"osters, Holger},
     title = {Difference prophet inequalities for 
 [0,1]
-valued i.i.d. random variables with cost for observations},
     journal = {Ann. Probab.},
     volume = {32},
     number = {1A},
     year = {2004},
     pages = { 3324-3332},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1107883355}
}

Kösters, Holger. Difference prophet inequalities for 
 [0,1]
-valued i.i.d. random variables with cost for observations. Ann. Probab., Tome 32 (2004) no. 1A, pp.  3324-3332. http://gdmltest.u-ga.fr/item/1107883355/