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)

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 by corr(t) or rho(t). x0, SDE parameters and dw(t, dt) should broadcast to vshape + (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

SDE

SDE.source_dw

wiener_source

wiener_SDE

Notes

x(t) is obtained via Euler-Maruyama numerical integration of the following equivalent SDE for a(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.