Records and Extremal Processes
Many natural questions about extremes need a stochastic process context for precise formulation. Imagine observing X 1, X 2,... at a rate of one per unit of time. Suppose while observing we compute the maxima M 1, M 2,.... We may ask how often or at what frequency does the maximum change. A change in the maximum means a record was observed, a record being a value larger than previous values. So the previous question is equivalent to asking how often records occur. Also, at what indices do records occur and do the actual record values have any pattern?
KeywordsPoint Process Weak Convergence Independent Increment Jump Time Markov Jump Process
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