Stochastic-process API

The public stochx.stochastic namespace contains explicit mathematical objects for stochastic-process coursework and applied probability.

Markov chains

• MarkovChain
• empirical_state_frequencies

See MarkovChain for transitions, communication classes, recurrence/transience, hitting and return times, stationarity, absorption and simulation.

Poisson processes

• PoissonProcess
• NonHomogeneousPoissonProcess

These objects cover counting-process probabilities and reproducible arrival-path simulation.

Continuous time

• ContinuousTimeMarkovChain
• CTMCPath
• BirthDeathProcess

The API uses generator matrices, continuous-time transition probabilities and explicit path objects.

Probability objects

• FiniteProbabilitySpace
• RandomVariable
• Partition

These form the basis for finite-space expectations and conditional expectation.

Information and martingales

• Filtration
• Martingale
• StoppingTime
• StoppedProcess

These objects model the information structure and stopping operations used in the corresponding mathematical theory.

Exceptions and validation

The public hierarchy includes StochXError, ValidationError, ProbabilityValidationError, MatrixValidationError, GeneratorValidationError and NumericalError.

The package prefers explicit failures over silent coercion. When a model violates its mathematical assumptions, the failure should identify the violated invariant as close to the API boundary as possible.

For conceptual explanations start with the Stochastic Processes User Guide.