aleatory.processes.WhiteNoise

class aleatory.processes.WhiteNoise(sigma=1.0, T=1.0, rng=None)

Gaussian Process White Noise

A centered Gaussian Process with covariance function given by

\[K(t, s) = \sigma^2 \delta(t - s)\]

where \(\delta\) is the Dirac delta function.

Notes

• The sample paths of this process are almost surely not continuous, and are not functions in the classical sense, but rather distributions.

Examples

from aleatory.processes import WhiteNoise
process = WhiteNoise(sigma=1.0, T=1.0)
fig = process.plot_paths_and_kernel(n=100, N=5, matrix_shape=True)
fig.show()

from aleatory.processes import WhiteNoise
process = WhiteNoise(sigma=1.0, T=1.0)
fig = process.draw(n=100, N=200, figsize=(12, 7))
fig.show()

__init__(sigma=1.0, T=1.0, rng=None)

Methods

__init__([sigma, T, rng])
covariance_function(times)
draw(n, N[, T, marginal, envelope, type, title])	Simulates and plots paths/trajectories from the instanced stochastic process.
estimate_covariances([times])
estimate_expectations()
estimate_quantiles(q)
estimate_stds()
estimate_variances()
get_marginal(time)
make_widget([cmap, matrix_shape])
marginal_expectation([times])
marginal_stds([times])
marginal_variance([times])
plot(n, N[, T, title, suptitle])	Simulates and plots paths/trajectories from the instanced stochastic process.
plot_covariance([times, colormap, ...])
plot_kernel([times, colormap, matrix_shape, ...])
plot_kernel3d([times, title])
plot_mean_function([T, n])
plot_mean_variance([times])
plot_paths_and_kernel(n, N[, T, cmap, ...])	Plots the paths of the process and the covariance kernel.
process_covariance([times])
process_expectation()
process_stds()
process_variance()
sample(n[, T])
sample_at(times)
simulate(n, N[, T])	Simulate paths/trajectories from the instanced stochastic process.
variance_function(times)

Attributes

T	End time of the process.
rng