Local maxima and distances between them in sequences of random variables

The subject of the report are the sequences of local maxima and distances between them in a sequence of independent identically distributed random variables. It is shown that sequence of pairs «distance and right local maxima» forms a Markov chain. This allowed to derive formulas for joint distribution of neighbouring local maxima and lengths of distances between them. Asymptotic behaviour of subsequence between two consequitive local maxima is studied. Joint distributions of numbers of intervals of specific length (between consequitive local maxima) is proven to be asymptotically normal.
For several dependent or not identically distributed random variables distributions between local maxima and probabilities for a given moment to be local maximum were studied.