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 |