Bounds for the variance of certain stationary point processes

For the variance of stationary renewal and alternating renewal processes N_n(·) the paper establishes upper and lower bounds of the form

$\text{?B}{}_1\text{?varN}{}_8\text{(0,x–Aλx?B}{}_2\text{(0<x<∞)< mtext="">, where <em>λ</em>=E<em>N</em>₈(0,1), with constants <em>A</em>, <em>B</em>₁ and <em>B</em>₂ that depend on the first three moments of the interval distributions for the processes concerned. These results are consistent with the value of the constant <em>A</em> for a general stationary point process suggested by Cox in 1963 [1].</x<∞)<>}$