m_pk {rlfsm} | R Documentation |
m(-p,k)
Description
defined as m_{p,k} := E[|\Delta_{k,k} X|^p]
for positive powers. When p is negative (-p is positive) the equality does not hold.
Usage
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{(\sigma \|h_k\|_{\alpha})^{-p}}{a_{-p}} \int_{\R} \exp(-|y|^{\alpha}) |y|^{-1+p} dy = \frac{2(\sigma \|h_k\|_{\alpha})^{-p}}{\alpha a_{-p}} \Gamma(p/\alpha)
References
Mazur S, Otryakhin D, Podolskij M (2020). “Estimation of the linear fractional stable motion.” Bernoulli, 26(1), 226–252. https://doi.org/10.3150/19-BEJ1124.
[Package rlfsm version 1.1.2 Index]