Strong approximations of renewal processes and their applications. (English) Zbl 0606.60037
Let \(\{(X_ n,Y_ n),n\geq 1\}\) be a sequence of random vectors in \(R^{d+1}\). Let \(U(t)=\sum_{1\leq i\leq t}X_ i\) and \(S(t)=\sum_{1\leq i\leq t}Y_ i\). The renewal process, being the inverse of U(t), is defined as \(N(t)=\inf (s:U(s)>t)\). A joint approximation of N(t) and S(N(t)) is obtained. Some applications of the main result are also given.
MSC:
| 60F15 | Strong limit theorems |
| 60K05 | Renewal theory |
| 60G50 | Sums of independent random variables; random walks |
| 60K25 | Queueing theory (aspects of probability theory) |
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