General Usage¶
Processes¶
This package offers a number of common discrete-time, continuous-time, and
noise process objects for generating realizations of stochastic processes as
numpy
arrays.
The diffusion processes are approximated using the Euler–Maruyama method.
Here are the currently supported processes and how to access their classes:
stochastic.processes
continuous
BesselProcess
BrownianBridge
BrownianExcursion
BrownianMeander
BrownianMotion
CauchyProcess
FractionalBrownianMotion
GammaProcess
GeometricBrownianMotion
InverseGaussianProcess
MixedPoissonProcess
MultifractionalBrownianMotion
PoissonProcess
SquaredBesselProcess
VarianceGammaProcess
WienerProcess
diffusion
DiffusionProcess (generalized)
ConstantElasticityVarianceProcess
CoxIngersollRossProcess
ExtendedVasicekProcess
OrnsteinUhlenbeckProcess
VasicekProcess
discrete
BernoulliProcess
ChineseRestaurantProcess
DirichletProcess
MarkovChain
MoranProcess
RandomWalk
noise
BlueNoise
BrownianNoise
ColoredNoise
PinkNoise
RedNoise
VioletNoise
WhiteNoise
FractionalGaussianNoise
GaussianNoise
Usage patterns¶
The sample() method¶
To use stochastic
, import the process you want and instantiate with the
required parameters. Every process class has a sample
method for generating
realizations. The sample
methods accept a parameter n
for the quantity
of steps in the realization, but others (Poisson, for instance) may take
additional parameters. Parameters can be accessed as attributes of the
instance.
from stochastic.processes.discrete import BernoulliProcess
bp = BernoulliProcess(p=0.6)
s = bp.sample(16)
success_probability = bp.p
Continuous processes provide a default parameter, t
, which indicates the
maximum time of the process realizations. The default value is 1. The sample
method will generate n
equally spaced increments on the
interval [0, t]
.
The sample_at() method¶
Some continuous processes also provide a sample_at()
method, in which a
sequence of time values can be passed at which the object will generate a
realization. This method ignores the parameter, t
, specified on
instantiation.
from stochastic.processes.continuous import BrownianMotion
bm = BrownianMotion(drift=1, scale=1, t=1)
times = [0, 3, 10, 11, 11.2, 20]
s = sample_at(times)
The times() method¶
Continuous-time processes also provide a method times()
which generates the
time values (using numpy.linspace
) corresponding to a realization of n
steps. This is particularly useful for plotting your samples.
import matplotlib.pyplot as plt
from stochastic.processes.continuous import FractionalBrownianMotion
fbm = FractionalBrownianMotion(hurst=0.7, t=1)
s = fbm.sample(32)
times = fbm.times(32)
plt.plot(times, s)
plt.show()
The algorithm option¶
Some processes provide an optional parameter algorithm
, in which one can
specify which algorithm to use to generate the realization using the
sample()
or sample_at()
methods. See class-specific documentation for
implementations.
from stochastic.processes.noise import FractionalGaussianNoise
fgn = FractionalGaussianNoise(hurst=0.6, t=1)
s = fgn.sample(32, algorithm='hosking')