aleatory.processes.RandomWalk

class aleatory.processes.RandomWalk(rng=None)

Simple Random Walk

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 \((\Omega, \mathcal{F}, \mathbb{P})\), such that

\[\mathbb{P}(Z_1 = 1) = p,\]

and

\[\mathbb{P}(Z_1 = -1) = 1-p,\]

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 a Simple Random Walk.

Constructor, Methods, and Attributes

__init__(rng=None)

Parameters:

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

Methods

__init__([rng])	parameter numpy.random.Generator rng: a custom random number generator
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()
marginal_expectation([times])
marginal_variance(times)
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