Stochastic Process API Reference#
StochasticProcess#
- class quantflow.sp.base.StochasticProcess#
Base class for stochastic processes in continuous time
- analytical_cdf(t: ndarray[Any, dtype[float64]] | float, x: ndarray[Any, dtype[float64]] | float) ndarray[Any, dtype[float64]] | float#
Analytical cdf of the process at time t
Implement if available
- analytical_mean(t: ndarray[Any, dtype[float64]] | float) ndarray[Any, dtype[float64]] | float#
Analytical mean of the process at time t
Implement if available
- analytical_pdf(t: ndarray[Any, dtype[float64]] | float, x: ndarray[Any, dtype[float64]] | float) ndarray[Any, dtype[float64]] | float#
Analytical pdf of the process at time t
Implement if available
- analytical_variance(t: ndarray[Any, dtype[float64]] | float) ndarray[Any, dtype[float64]] | float#
Analytical variance of the process at time t
Implement if available
- characteristic(t: ndarray[Any, dtype[float64]] | float, u: int | float | complex | ndarray | Series) int | float | complex | ndarray | Series#
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[Any, dtype[float64]] | 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[Any, dtype[float64]] | float) int | float | complex | ndarray | Series#
Convexity correction for the process
- model_computed_fields: ClassVar[Dict[str, ComputedFieldInfo]] = {}#
A dictionary of computed field names and their corresponding ComputedFieldInfo objects.
- model_config: ClassVar[ConfigDict] = {'extra': 'forbid'}#
Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].
- model_fields: ClassVar[Dict[str, FieldInfo]] = {}#
Metadata about the fields defined on the model, mapping of field names to [FieldInfo][pydantic.fields.FieldInfo] objects.
This replaces Model.__fields__ from Pydantic V1.
StochasticProcess1d#
IntensityProcess#
- 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
- abstract integrated_log_laplace(t: ndarray[Any, dtype[float64]] | float, u: int | float | complex | ndarray | Series) int | float | complex | ndarray | Series#
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_computed_fields: ClassVar[Dict[str, ComputedFieldInfo]] = {}#
A dictionary of computed field names and their corresponding ComputedFieldInfo objects.
- model_config: ClassVar[ConfigDict] = {'extra': 'forbid'}#
Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].
- model_fields: ClassVar[Dict[str, FieldInfo]] = {'kappa': FieldInfo(annotation=float, required=False, default=1.0, description='Mean reversion speed', metadata=[Gt(gt=0)]), 'rate': FieldInfo(annotation=float, required=False, default=1.0, description='Instantaneous initial rate', metadata=[Gt(gt=0)])}#
Metadata about the fields defined on the model, mapping of field names to [FieldInfo][pydantic.fields.FieldInfo] objects.
This replaces Model.__fields__ from Pydantic V1.