m_pk: m(-p,k)

Description Usage Arguments Details References

View source: R/functions_for_estimates.r

Description

defined as m_{p,k} := E[|Δ_{k,k} X|^p] for positive powers. When p is negative (-p is positive) the equality does not hold.

Usage

1
m_pk(k, p, alpha, H, sigma)

Arguments

k

increment order

p

a positive number

alpha

self-similarity parameter of alpha stable random motion.

H

Hurst parameter

sigma

Scale parameter of lfsm

Details

The following identity is used for computations:

m_{-p,k} = \frac{(σ \|h_k\|_{α})^{-p}}{a_{-p}} \int_{\R} \exp(-|y|^{α}) |y|^{-1+p} dy = \frac{2(σ \|h_k\|_{α})^{-p}}{α a_{-p}} Γ(p/α)

References

\insertRef

MOP18rlfsm


rlfsm documentation built on April 16, 2021, 5:06 p.m.

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