Beschreibung:
<jats:p>We define a vector-valued <jats:italic>scheduled maxima</jats:italic> sequence <jats:italic>
<jats:bold>M</jats:bold>
</jats:italic> by considering simultaneously the maxima of several i.i.d. sequences, with the number of observations considered from each sequence at any time determined by a random scheduling sequence <jats:italic>
<jats:bold>J.</jats:bold>
</jats:italic> It is shown that the max-min (vector) sequence <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0021900200045915_inline1" xlink:type="simple" /> derived from i.i.d. <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0021900200045915_inline2" xlink:type="simple" /> can be represented as a mixture of scheduled maxima sequences, giving results for this sequence and the range <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0021900200045915_inline3" xlink:type="simple" /> A functional limit theorem for the scheduled maxima sequence shows convergence to independent extremal processes. Embedding in a scheduled extremal process gives strong laws, central limit theorems, and laws of the iterated logarithm for the record time of the scheduled maxima sequence, and hence for the max-min sequence and the range.</jats:p>