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, $\mathrm{\Gamma }(t;1,\nu )$, the variance gamma process will follow:

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

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

References

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