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[1] It also must be increasing, almost surely.[1] or an additive process[2].
Definition
A subordinator is an increasing (a.s.) Lévy process or additive process. [3][2]
Examples
The variance gamma process can be described as a Brownian motion subject to a gamma subordinator.[1] 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.[1]
References
- ^ a b c d Applebaum, D. "Lectures on Lévy processes and Stochastic calculus, Braunschweig; Lecture 2: Lévy processes" (PDF). University of Sheffield. pp. 37–53.
- ^ a b Li, Jing; Li, Lingfei; Zhang, Gongqiu (2017). "Pure jump models for pricing and hedging VIX derivatives". Journal of Economic Dynamics and Control. 74. doi:10.1016/j.jedc.2016.11.001.
- ^ Lévy Processes and Stochastic Calculus (2nd ed.). Cambridge: Cambridge University Press. 2009-05-11. ISBN 9780521738651.
 | This probability-related article is a stub. You can help Wikipedia by expanding it. |