Stochastic Process

Stochastic Process#

This page gives an overview of all Stochastic Processes available in the library.

class quantflow.sp.base.StochasticProcess

Base class for stochastic processes in continuous time

Methods:

`analytical_cdf`	Analytical cdf of the process at time t
`analytical_mean`	Analytical mean of the process at time t
`analytical_pdf`	Analytical pdf of the process at time t
`analytical_variance`	Analytical variance of the process at time t
`characteristic`	Characteristic function at time t for a given input parameter
`characteristic_exponent`	Characteristic exponent at time t for a given input parameter
`convexity_correction`	Convexity correction for the process
`sample`	Generate random `Paths` from the process.
`sample_from_draws`	Sample `Paths` from the process given a set of draws

Attributes:

model_config

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

analytical_cdf(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float, x: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Analytical cdf of the process at time t

Implement if available

analytical_mean(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Analytical mean of the process at time t

Implement if available

analytical_pdf(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float, x: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Analytical pdf of the process at time t

Implement if available

analytical_variance(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Analytical variance of the process at time t

Implement if available

Characteristic function at time t for a given input parameter

The characteristic function represents the Fourier transform of the probability density function

\[\phi = {\mathbb E} \left[e^{i u x_t}\right]\]

Parameters:

t – time horizon
u – characteristic function input parameter

abstract characteristic_exponent(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float, u: int | float | complex | ndarray | Series) → int | float | complex | ndarray | Series: Characteristic exponent at time t for a given input parameter

convexity_correction(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → int | float | complex | ndarray | Series: Convexity correction for the process

model_config: ClassVar[ConfigDict] = {'extra': 'forbid'}: Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

abstract sample(n: int, time_horizon: float = 1, time_steps: int = 100) → Paths

Generate random Paths from the process.

Parameters:

n – number of paths
time_horizon – time horizon
time_steps – number of time steps to arrive at horizon

abstract sample_from_draws(draws: Paths, *args: Paths) → Paths: Sample Paths from the process given a set of draws

class quantflow.sp.base.StochasticProcess1D

Base class for 1D stochastic process in continuous time

frequency_range(std: float, max_frequency: float | None = None) → Bounds: Maximum frequency when calculating characteristic functions

model_config: ClassVar[ConfigDict] = {'extra': 'forbid'}: Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

support(mean: float, std: float, points: int) → ndarray[tuple[int, ...], dtype[floating[Any]]]: Support of the process at time t

class quantflow.sp.base.IntensityProcess(*, rate: Annotated[float, Gt(gt=0)] = 1.0, kappa: Annotated[float, Gt(gt=0)] = 1.0)

Base class for mean reverting 1D processes which can be used as stochastic intensity

The log-Laplace transform of the cumulative process:

\[e^{\phi_{t, u}} = {\mathbb E} \left[e^{i u \int_0^t x_s ds}\right]\]

Parameters:

t – time horizon
u – frequency

model_config: ClassVar[ConfigDict] = {'extra': 'forbid'}: Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].