ABSTRACT
This chapter discusses the limiting distribution of the sojourn time a rising level u is obtained for levels. It provides a strikingly different result which is completely unrelated to the other results: The normal limit arises as a consequence of long-range dependence rather than long-range independence. The chapter examines an application of the result to a method for the estimation of the tail of the spectral distribution based on sojourns a set of rising levels. It explains the estimation of the tail of the spectral distribution by means of observed sojourn times a series of rising levels and deals with the case where the level rises more slowly. The sojourns the level are longer and more frequent, and the local behavior of the sample function determines one of the normalizing functions, but not the form of the limiting distribution, which turns out to be normal.
