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.
m_pk(k, p, alpha, H, sigma)increment order
a positive number
self-similarity parameter of alpha stable random motion.
Hurst parameter
Scale parameter of lfsm
The following identity is used for computations: $$m_{-p,k} = \frac{(\sigma \|h_k\|_{\alpha})^{-p}}{a_{-p}} \int_{\R} \exp(-|y|^{\alpha}) |y|^{-1+p} dy = \frac{2(\sigma \|h_k\|_{\alpha})^{-p}}{\alpha a_{-p}} \Gamma(p/\alpha)$$
MOP18rlfsm