systems.base.numerical_integration.stochastic.CustomBrownianPath

systems.base.numerical_integration.stochastic.CustomBrownianPath(t0, t1, dW)

Custom Brownian motion that uses provided dW increments.

This implements Diffrax’s AbstractPath interface to allow user-specified noise instead of generating random noise.

Uses Equinox Module for proper JAX/Diffrax integration.

Attributes

Name	Type	Description
t0	ScalarLike	Start time
t1	ScalarLike	End time
dW	ArrayLike	Brownian increment for interval (t0, t1) Shape: (nw,) for the noise dimensions

Examples

>>> # Zero noise for deterministic testing
>>> dW = jnp.zeros(1)
>>> brownian = CustomBrownianPath(0.0, 0.01, dW)
>>>
>>> # Custom noise pattern
>>> dW = jnp.array([0.5])
>>> brownian = CustomBrownianPath(0.0, 0.01, dW)

Methods

Name	Description
evaluate	Evaluate Brownian increment between t0 and t1.

evaluate

systems.base.numerical_integration.stochastic.CustomBrownianPath.evaluate(
    t0,
    t1=None,
    left=True,
)

Evaluate Brownian increment between t0 and t1.

For custom noise, we provide the exact increment for our interval. Diffrax will call this to get dW values.

This method must be JIT-compatible, so we use jnp.where() instead of Python if statements to avoid tracer boolean conversion errors.

Parameters

Name	Type	Description	Default
t0	ScalarLike	Start time of query	required
t1	Optional[ScalarLike]	End time of query (if None, return value at t0)	None
left	bool	Whether to use left or right limit	True

Returns

Name	Type	Description
	Array	Brownian increment or value (JAX array for Diffrax compatibility)