Subordinator (mathematics)

In probability theory, a subordinator is a stochastic process that is non-negative and whose increments are stationary and independent.[1] Subordinators are a special class of Lévy process that play an important role in the theory of local time.[2] In this context, subordinators describe 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[3] It also must be increasing, almost surely,[3] or an additive process.[4]

  1. ^ Cite error: The named reference KallebergFoundations290 was invoked but never defined (see the help page).
  2. ^ Cite error: The named reference KallenbergMeasures651 was invoked but never defined (see the help page).
  3. ^ a b Applebaum, D. "Lectures on Lévy processes and Stochastic calculus, Braunschweig; Lecture 2: Lévy processes" (PDF). University of Sheffield. pp. 37–53.
  4. ^ 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.