types.trajectories.NoiseSequence

types.trajectories.NoiseSequence

Noise/disturbance sequence for stochastic simulation.

Time series of random disturbances in stochastic systems.

Shapes: - Single sequence: (n_steps, nw) IID noise samples

• Batched sequences: (n_steps, batch, nw) Independent noise for each trajectory

Distribution: - Discrete stochastic: w[k] ~ N(0, I) - Continuous SDE: dW[k] ~ N(0, dt*I) (Brownian increments)

Examples

>>> # Standard normal noise for discrete system
>>> w_seq: NoiseSequence = np.random.randn(100, 2)
>>> trajectory = system.simulate_stochastic(x0, u_seq, w_seq)
>>> 
>>> # Brownian increments for continuous SDE
>>> dt = 0.01
>>> n_steps = 1000
>>> dW: NoiseSequence = np.random.randn(n_steps, 2) * np.sqrt(dt)
>>> 
>>> # Reproducible simulation with seed
>>> np.random.seed(42)
>>> w_seq: NoiseSequence = np.random.randn(100, 3)
>>> 
>>> # Batched Monte Carlo simulation
>>> n_trials = 1000
>>> w_batch: NoiseSequence = np.random.randn(100, n_trials, 2)
>>> trajectories_mc = system.simulate_stochastic_batch(x0, u_seq, w_batch)
>>> 
>>> # Colored noise (correlated)
>>> # First generate white noise, then filter
>>> w_white = np.random.randn(1000, 2)
>>> # Apply low-pass filter for colored noise
>>> from scipy.signal import lfilter
>>> b, a = [0.1, 0.9], [1.0]
>>> w_colored: NoiseSequence = lfilter(b, a, w_white, axis=0)