A Simple Analytic Proof of the Pollaczek-Wendel Identity for Ordered Partial Sums
Smit, Jos H. A. De
Ann. Probab., Tome 1 (1973) no. 5, p. 348-351 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
In this note we prove an identity due to Pollaczek (1952) and Wendel (1960). The identity describes the distributions of ordered partial sums of independent identically distributed random variables and thus generalizes Spitzer's identity. Our proof follows from a simple analytic argument applying a kind of Wiener-Hopf decomposition. We also give an extension of the Pollaczek-Wendel identity.
Publié le : 1973-04-14
Classification:  
@article{1176996991,
     author = {Smit, Jos H. A. De},
     title = {A Simple Analytic Proof of the Pollaczek-Wendel Identity for Ordered Partial Sums},
     journal = {Ann. Probab.},
     volume = {1},
     number = {5},
     year = {1973},
     pages = { 348-351},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996991}
}

Smit, Jos H. A. De. A Simple Analytic Proof of the Pollaczek-Wendel Identity for Ordered Partial Sums. Ann. Probab., Tome 1 (1973) no. 5, pp.  348-351. http://gdmltest.u-ga.fr/item/1176996991/