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Two consistent estimators for the Skew Brownian motion

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Table 1: Statistics of the MLE θ n with ∆t = 0.1 , T = 102.4 , θ ∈ { 0, 0.3, 0.7, 0.9 } and n = 2 10 = 1024 observations of { X k∆t }
Figure 1: Density of the difference θ n − θ with ∆t = 0.1, T = 102.4, θ ∈ { 0, 0.3, 0.7, 0.9 } and n = 2 k points sampled at equal distance from the observations { X k∆t }
Figure 2: Density of the rescaled difference n 1/4 (θ n − θ) with ∆t = 0.1 , T = 28 000, θ ∈ { 0, 0.3, 0.7, 0.9 } and n = 2 k points sampled at equal distance from the observations { X k∆t }
Figure 3: Estimation of b κ obtained by fitting the distribution of n 1/4 (θ n − θ) against the one of b κΥ using the Kolmogorov-Smirnov statistics for θ ∈ { 0, 0.1,

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