Seismic inverse Q filtering

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.

Examples

The variance gamma process can be described as a Brownian motion subject to a gamma subordinator. 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.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Template:Probability-stub