sigalg 0.1.1

A Python package for measure-theoretic probability theory.

SigAlg

A Python package for finite, measure-theoretic probability theory and stochastic processes. The library emphasizes mathematical fidelity while remaining practical for simulations and numerical experiments.

This package is under active development. Extensive documentation is coming soon.

Installation

pip install sigalg

Quick Examples

Build and simulate a random walk:

import matplotlib.pyplot as plt

from sigalg.core import Time
from sigalg.processes import RandomWalk

# Create a random walk with 100 discrete time steps
T = Time.discrete(length=100)
X = RandomWalk(p=0.7, time=T)

# Simulate 10 trajectories
X.from_simulation(n_trajectories=10, random_state=42)

# Plot trajectories
_, ax = plt.subplots(figsize=(7, 4))
X.plot_trajectories(ax=ax)
plt.show()

Compute conditional expectation of a random variable with respect to a $\sigma$-algebra:

from sigalg.core import (
    Operators,
    ProbabilityMeasure,
    RandomVariable,
    SampleSpace,
    SigmaAlgebra,
)

# Create a sample space with 4 outcomes, labeled 0, 1, 2, 3
Omega = SampleSpace().from_sequence(size=4)

# Define a probability measure by assigning probabilities to each outcome
P = ProbabilityMeasure(sample_space=Omega).from_dict(
    {
        0: 0.2,  # P(0) = 0.2
        1: 0.3,  # P(1) = 0.3
        2: 0.3,  # P(2) = 0.3
        3: 0.2,  # P(3) = 0.2
    }
)

# Define a random variable by assigning values to each outcome
X = RandomVariable(domain=Omega, name="X").from_dict(
    {
        0: 1,  # X(0) = 1
        1: 2,  # X(1) = 2
        2: 8,  # X(2) = 8
        3: 3,  # X(3) = 3
    }
)

# Sigma-algebras are defined by partitioning the sample space into sets called atoms
F = SigmaAlgebra(sample_space=Omega, name="F").from_dict(
    {
        0: "A",  # outcome 0 is in atom A
        1: "A",  # outcome 1 is in atom A
        2: "B",  # outcome 2 is in atom B
        3: "B",  # outcome 3 is in atom B
    }
)

# Compute conditional expectation E(X|F)
E_X_F = Operators.expectation(rv=X, sigma_algebra=F, probability_measure=P)
print(E_X_F)

Random vector 'E(X|F)':
        E(X|F)
sample        
0          1.6
1          1.6
2          6.0
3          6.0

Author

John Myers