3.5.3. sdepy.ornstein_uhlenbeck_process¶
-
class
sdepy.
ornstein_uhlenbeck_process
(paths=1, vshape=(), dtype=None, rng=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)[source]¶ 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 bycorr(t)
orrho(t)
.x0
, SDE parameters anddw(t, dt)
should broadcast tovshape + (paths,)
.Parameters: - paths, vshape, dtype, rng, 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.
Attributes: - See SDE class documentation.
Methods
See SDE class documentation.