Simulate 100 paths for the following diffusions given by their SDES on [0,1] using the Euler-Maruyama...

  

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Simulate 100 paths for the following diffusions given by their SDES on [0,1] using the Euler-Maruyama scheme and the Milstein scheme for a discretization of 0.01. (a) Geometric Brownian motion: ds, = S, dB, + (+s, dt, S = 1, +u+ for -1/2, = -2, and = 0. (b) Ornstein-Uhlenbeck process: dx=-x, dt + dB, X = 1. Simulate 100 paths for the following diffusions given by their SDES on [0,1] using the Euler-Maruyama scheme and the Milstein scheme for a discretization of 0.01. (a) Geometric Brownian motion: ds, = S, dB, + (+s, dt, S = 1, +u+ for -1/2, = -2, and = 0. (b) Ornstein-Uhlenbeck process: dx=-x, dt + dB, X = 1.