Mean sqrt(alpha_bar_t) * x_0, variance 1 - alpha_bar_t.
No simulation is needed to check it.
Examples
forward_corrupt(x0 = c(1, 2, 3), alpha_bar_t = 0.81)$mean
#> [1] 0.9 1.8 2.7
Mean sqrt(alpha_bar_t) * x_0, variance 1 - alpha_bar_t.
No simulation is needed to check it.
forward_corrupt(x0 = c(1, 2, 3), alpha_bar_t = 0.81)$mean
#> [1] 0.9 1.8 2.7