aleatory.processes.BrownianBridge

class aleatory.processes.BrownianBridge(initial=0.0, end=0.0, T=1.0, rng=None)

Brownian Bridge

Definition

A Brownian bridge is a continuous-time stochastic process \(\{B_t : t \geq 0\}\) whose probability distribution is the conditional probability distribution of a standard Wiener process (Brownian Motion) \(\{W_t : t \geq 0\}\) subject to the condition that \(W(T) = 0\), so that the process is pinned to the same value at both \(t = 0\) and \(t = T\). More specifically,

\[B_t = (W_t | W_T = 0), \ \ \ \ t\in (0,T].\]

More generally, a Brownian Bridge is subject to the conditions \(W(0) = a\) and \(W(T) = b\).

Constructor, Methods, and Attributes

__init__(initial=0.0, end=0.0, T=1.0, rng=None)

Parameters:

• initial (float) – initial condition

• end (float) – end condition

• T (float) – the right hand endpoint of the time interval \([0,T]\) for the process

• rng (numpy.random.Generator) – a custom random number generator

Methods

__init__([initial, end, T, rng])	param float initial: initial condition
draw(n, N[, envelope, title, suptitle])	Simulates and plots paths/trajectories from the instanced stochastic process.
estimate_covariances([times])
estimate_expectations()
estimate_quantiles(q)
estimate_stds()
estimate_variances()
get_marginal(t)
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, title])
plot_kernel([times, colormap, matrix_shape, ...])
plot_kernel3d([times, title])
plot_mean_variance(times, **fig_kw)
plot_paths_and_kernel(n, N[, T, title, ...])	Plots the paths of the process and the covariance kernel.
process_covariance([times])
process_expectation()
process_stds()
process_variance()
sample(n)	Generates a discrete time sample from a Brownian Motion instance.
sample_at(times)	Generates a sample from a Brownian motion at the specified times.
simulate(n, N[, T])	Simulate paths/trajectories from the instanced stochastic process.

Attributes

T	End time of the process.
drift
end
initial
rng
scale