The impact of periodicity on the zero-crossings of random functions
Wilson, Lorna Rachel Maven (2015) The impact of periodicity on the zero-crossings of random functions. PhD thesis, University of Nottingham.
Continuous random processes are used to model a huge variety of real world phenomena. In particular, the zero-crossings of such processes find application in modelling processes of diffusion, meteorology, genetics, finance and applied probability. Understanding the zero-crossings behaviour improves prediction of phenomena initiated by a threshold crossing, as well as extremal problems where the turning points of the process are of interest. To identify the Probability Density Function (PDF) for the times between successive zero-crossings of a stochastic process is a challenging problem with a rich history.
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