Identification of Nonstandard Multifractional Brownian Motions under White Noise by Multiscale Local Variations of Its Sample Paths

Table 1

Average mean squared error for the S-K-var, K-var-VC, and K-var methods in various settings of variance constant 𝐶 and SNR levels based on 1000 sample paths of 𝑊^′(𝑡) for each of step-function and straight-line 𝐻(𝑡). The asterisk marks show that S-K-var outperformed the other methods.

Parameters	Average mean squared error
	Step-function 𝐻(𝑡)			Straight-line 𝐻(𝑡)
	S-K-var	K-var-VC	K-var	S-K-var	K-var-VC	K-var
𝐶=1, SNR 10	31.54*	178.6	107.1	84.62	215.5	81.31
30	22.85*	89.64	64.59	25.48	147.8	23.53
∞	9.940*	26.31	48.16	.8242*	9.508	.9376
𝐶=4, SNR 10	15.56*	212.5	82.29	46.16*	176.9	175.2
30	4.406*	152.2	39.91	36.11*	92.07	120.2
∞	.9706*	10.00	8.173	10.04*	24.73	93.21
𝐶=10, SNR 10	61.80*	178.2	281.5	89.94*	216.5	223.9
30	55.97*	87.35	237.0	42.21*	150.9	144.6
∞	33.86*	26.08	193.1	1.425*	9.288	77.32