2.5.3. sdepy.ornstein_uhlenbeck_process

class sdepy.ornstein_uhlenbeck_process(paths=1, vshape=(), dtype=None, steps=None, i0=0, info=None, getinfo=True, method='euler', x0=0., theta=0., k=1., sigma=1., dw=None, corr=None, rho=None)

Ornstein-Uhlenbeck process (mean-reverting Brownian motion).

Generates a process x(t) that solves the following SDE:

dx(t) = k(t)*(theta(t) - x(t))*dt + sigma(t)*dw(t, dt)

where dw(t, dt) are standard Wiener process increments with correlation matrix specified by corr(t) or rho(t). x0, SDE parameters and dw(t, dt) should broadcast to vshape + (paths,).

Parameters:

paths, vshape, dtype, steps, i0, info, getinfo, method

See SDE class documentation.

x0 : array-like

Initial condition.

theta, k, sigma : array-like, or callable

SDE parameters.

dw, corr, rho

Specification of stochasticity source of Wiener process increments. See SDE.source_dw documentation.

Returns:

x : process

Once instantiated as p, p(timeline) performs the integration along the given timeline, based on parameters of instantiation, and returns the resulting process.

See also

SDE

SDE.source_dw

wiener_source

ornstein_uhlenbeck_SDE

Attributes:

See SDE class documentation.

Methods

See SDE class documentation.