Generate realizations of stochastic processes
Project description
A python package for generating realizations of stochastic processes.
Installation
The stochastic package is available on pypi and can be installed using pip
pip install stochastic
Dependencies
Stochastic uses numpy for many calculations and scipy for sampling specific random variables.
Processes
This package offers a number of common discretetime, continuoustime, 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 their class references within the package.
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
Sampling
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].
Sampling at specific times
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 = bm.sample_at(times)
Sample times
Continuous 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()
Specifying an algorithm
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 the documentation for processspecific implementations.
from stochastic.processes.noise import FractionalGaussianNoise
fgn = FractionalGaussianNoise(hurst=0.6, t=1)
s = fgn.sample(32, algorithm='hosking')
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