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On a class of spatial renewal processes: Renewal processes synchronization probabilities
Statistics & Probability Letters, 2020Let \(X_{i}=(X_{i}^{(1)},\dots,X_{i}^{(d)}),i=1,2,\dots\) denote i.i.d. nonnegative random vectors and let \(S_{n}=(S_{n}^{(1)},\dots,S_{n}^{(d)})\) denote the sequence of partial sums. In renewal theory one studies the process \(N(B)=\) the number of \(n\) so that \(S_{n}\in B\), and the renewal measure \(M_{N}(B)=EN(B)\).
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