A Counterexample in Renewal Theory
Root, David
Ann. Math. Statist., Tome 42 (1971) no. 6, p. 1763-1766 / Harvested from Project Euclid
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The purpose of this note is to give a counterexample to the following statement. Let $Y_1, Y_2, \cdots$ be i.i.d rv with distribution function $F$ and $P\lbrack Y_1 \geqq 0\rbrack = 1$. For any set $A \subset \lbrack 0, \infty)$ let $U(A) = \sum^\infty_{k=0} F^{\ast k}(A)$ be the usual renewal measure. If $A \subset \lbrack 0, \infty)$ and $U(A) = +\infty$ then there is a renewal in $A$ almost surely.
Publié le : 1971-10-14
Classification:  
@article{1177693179,
     author = {Root, David},
     title = {A Counterexample in Renewal Theory},
     journal = {Ann. Math. Statist.},
     volume = {42},
     number = {6},
     year = {1971},
     pages = { 1763-1766},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177693179}
}

Root, David. A Counterexample in Renewal Theory. Ann. Math. Statist., Tome 42 (1971) no. 6, pp.  1763-1766. http://gdmltest.u-ga.fr/item/1177693179/