rlfsm (version 1.1.2)

h_kr: Function h_kr

Description

Function $h_{k,r}:R\to R$ is given by $$h_{k,r}(x)=\sum _{j=0}^k(-1{)}^j(\genfrac{}{}{0ex}{}{k}{j})(x-rj{)}_{+}^{H-1/\alpha },x\in R$$

Usage

h_kr(k, r, x, H, alpha, l = 0)

Arguments

k

order of the increment, a natural number

r

difference step, a natural number

x

real number

H

Hurst parameter

alpha

self-similarity parameter of alpha stable random motion.

l

a value by which we shift x. Is used for computing function f_.+l and is passed to integrate function.

References

MOP18rlfsm

Examples

#### Plot h_kr ####
s<-seq(0,10, by=0.01)
h_val<-sapply(s,h_kr, k=5, r=1, H=0.3, alpha=1)
plot(s,h_val)