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11.5.2.4. astroML.time_series.generate_damped_RW

astroML.time_series.generate_damped_RW(t_rest, tau=300.0, z=2.0, xmean=0, SFinf=0.3, random_state=None)

Generate a damped random walk light curve

This uses a damped random walk model to generate a light curve similar to that of a QSO [R19].

Parameters :

t_rest : array_like

rest-frame time. Should be in increasing order

tau : float

relaxation time

z : float

redshift

xmean : float (optional)

mean value of random walk; default=0

SFinf : float (optional

Structure function at infinity; default=0.3

random_state : None, int, or np.random.RandomState instance (optional)

random seed or random number generator

Returns :

x : ndarray

the sampled values corresponding to times t_rest

Notes

The differential equation is (with t = time/tau):

dX = -X(t) * dt + sigma * sqrt(tau) * e(t) * sqrt(dt) + b * tau * dt

where e(t) is white noise with zero mean and unit variance, and

Xmean = b * tau SFinf = sigma * sqrt(tau / 2)

so

dX(t) = -X(t) * dt + sqrt(2) * SFint * e(t) * sqrt(dt) + Xmean * dt

References

[R19](1, 2) Kelly, B., Bechtold, J. & Siemiginowska, A. (2009) Are the Variations in Quasar Optical Flux Driven by Thermal Fluctuations? ApJ 698:895 (2009)