fBm satisfies f(lambda t) equal in distribution to lambda^H f(t), so
its variances obey E f(lambda t)^2 = lambda^(2H) E f(t)^2 EXACTLY –
this is an identity read straight off the kernel (11.6), not a limit.
Self-similarity is what makes the length-scale rescaling of section
11.5 equivalent to a change of smoothness index.
Usage
Ghosalselfsimgp(H = 0.6, lam = 3, t = 0.2)
Arguments
- H
Hurst index, in (0, 1).
- lam
Scaling factor, positive.
- t
Time point, positive.
Value
List with estimate (the variance ratio),
expected, gap, method.
Details
Formula: ((lambda t)^(2H)) / (t^(2H)) = lambda^(2H).
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 11.5.1.
Examples
Ghosalselfsimgp()
#> $estimate
#> [1] 3.737193
#>
#> $expected
#> [1] 3.737193
#>
#> $gap
#> [1] 0
#>
#> $method
#> [1] "fBm self-similarity (GvdV 2017 sec. 11.5.1)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
