Point stochastic processes

Introduction

A point process is a stochastic process {N(t) = number of occurrences by time t} which describes the appearance of a sequence of instant random events in time. Usually (though not always) intervals between two neighboring events are considered to be independently distributed. A process of this type is called a point process with restricted memory . If times between occurrences (e.g., called interarrival times in queueing theory, etc.) are a sequence of independent and identically distributed (i.i.d.) random variables, the point process is called a renewal or recurrent point process. The Poisson process represents a particular case of a renewal process in that the intervals between occurrences are identically exponentially distributed (Cox and Isham, 1980; Franken et al., 1981)

Point processes of a special type can be formed by two random variables which alternate with the sequence X ₁, Y ₁, X ₂, Y ₂,...and so on. Such a process is called alternating point process —more...