Subordinator (mathematics)
In the mathematics of probability, a subordinator is a concept related to stochastic processes. A subordinator is itself a stochastic process of the evolution of time within another stochastic process, the subordinated stochastic process. In other words, a subordinator will determine the random number of "time steps" that occur within the subordinated process for a given unit of chronological time.
In order to be a subordinator a process must be a Lévy process It also must be increasing, almost surely. or an additive process.Definition
A subordinator is an increasing Lévy process or additive process.Examples
The variance gamma process can be described as a Brownian motion subject to a gamma subordinator. If a Brownian motion,, with drift is subjected to a random time change which follows a gamma process,, the variance gamma process will follow:
The Cauchy process can be described as a Brownian motion subject to a Lévy subordinator.
