Subordinator (mathematics)

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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.[1] It also must be increasing, almost surely.[1]

Examples[edit]

The variance gamma process can be described as a Brownian motion subject to a gamma subordinator.[1] If a Brownian motion, W(t), with drift \theta t is subjected to a random time change which follows a gamma process, \Gamma(t; 1, \nu), the variance gamma process will follow:


 X^{VG}(t; \sigma, \nu, \theta) \;:=\; \theta \,\Gamma(t; 1, \nu) + \sigma\,W(\Gamma(t; 1, \nu)).

The Cauchy process can be described as a Brownian motion subject to a Lévy subordinator.[1]

References[edit]