m_pk {rlfsm} | R Documentation |
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.
m_pk(k, p, alpha, H, sigma)
k |
increment order |
p |
a positive number |
alpha |
self-similarity parameter of alpha stable random motion. |
H |
Hurst parameter |
sigma |
Scale parameter of lfsm |
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)
Mazur S, Otryakhin D, Podolskij M (2018). “Estimation of the linear fractional stable motion.” Aarhus University.