aleatory.processes.GeneralRandomWalk#

class aleatory.processes.GeneralRandomWalk(step_dist=None, step_args=None, step_kwargs=None, normalised=False, rng=None)[source]#

General Random Walk#

../_images/gen_random_walk_draw.png

Notes#

Let \(\{Z_i, i \geq 1\}\) be a sequence of real-valued independent an identically distributed (i.i.d.) random variables defined on a probability space \((\Omega, \mathcal{F}, \mathbb{P})\). Then, the stochastic process \(\{X_n , n\geq 0\}\), defined as \(X_0 =0\), and

\[X_n = \sum_{i=1}^n Z_i, \qquad \forall n\geq 1,\]

is called random walk, or more precisely one-dimensional random walked based on \(\{Z_i, i \geq 1\}\).

Constructor, Methods, and Attributes#

__init__(step_dist=None, step_args=None, step_kwargs=None, normalised=False, rng=None)[source]#
Parameters:

  • step_dist – an object representing the random variable \(Z_i\) above (e.g.scipy.stats.norm)

  • step_args – arguments (if any) to pass to the chosen step distribution

  • step_kwargs – keyword arguments (if any) to pass to the chosen step distribution

  • normalised (bool) – normalised or not

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

Methods

__init__([step_dist, step_args, ...])

parameter step_dist:

an object representing the random variable \(Z_i\) above (e.g.scipy.stats.norm)

draw(n, N[, marginal, envelope, mode, ...])

Simulates and plots paths/trajectories from the instanced stochastic process.

estimate_covariances([times])

estimate_expectations()

estimate_quantiles(q)

estimate_stds()

estimate_variances()

plot(*args, n, N[, title, suptitle])

Simulates and plots paths/trajectories from the instanced stochastic process.

process_covariance([times])

process_expectation()

process_stds()

process_variance()

sample(n)

simulate(n, N[, T])

Simulate paths/trajectories from the instanced stochastic process.

Attributes

T

End time of the process.

rng