2.5.2. sdepy.lognorm_process¶
-
class
sdepy.
lognorm_process
(paths=1, vshape=(), dtype=None, steps=None, i0=0, info=None, getinfo=True, method='euler', x0=1., mu=0., sigma=1., dw=None, corr=None, rho=None)[source]¶ Lognormal process.
Generates a process
x(t)
that solves the following SDE:dx(t) = mu(t)*x(t)*dt + sigma(t)*x(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,)
.x0
should be positive.Parameters: - paths, vshape, dtype, steps, i0, info, getinfo, method
See
SDE
class documentation.- x0 : array-like
Initial condition.
- mu, 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
Notes
x(t)
is obtained via Euler-Maruyama numerical integration of the following equivalent SDE fora(t) = log(x(t))
:da(t) = (mu(t) - sigma(t)**2/2)*dt + sigma(t)*dw(t, dt)
Attributes: - See SDE class documentation.
Methods
See SDE class documentation.