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An example of Wold’s point processes with Markov-dependent intervals. (English) Zbl 0391.60052

Summary: Wold’s point process is briefly introduced and its forward equation is derived in terms of an integro-differential equation which is used to obtain the ‘renewal’ function. An example of this family of processes is given in which each interval is exponentially distributed. The theory of diagonal expansion for a bivariate distribution is used to obtain the numerical estimate of the spectrum of counts.

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60J05 Discrete-time Markov processes on general state spaces
60G10 Stationary stochastic processes
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