StoppingTime
StoppingTime represents a discrete stopping time with values in \(\mathbb N\cup\{\infty\}\) with respect to a filtration. The construction enforces the finite-time stopping-time condition from the course model.
Constructor
StoppingTime(space, values, filtration)
Parameters
| Parameter | Description |
|---|---|
space |
Underlying FiniteProbabilitySpace. |
values |
Outcome-to-stopping-time mapping. |
filtration |
Filtration with respect to which the stopping condition is checked. |
Class methods
from_values(space, values, filtration)— explicit construction helper from outcome-wise values.
Properties
| Property | Meaning |
|---|---|
space |
Underlying probability space. |
values |
Outcome-wise stopping times. |
filtration |
Filtration used for the definition. |
Methods
minimum(other)— construct \(T\wedge S\).maximum(other)— construct \(T\vee S\).add(other)— construct \(T+S\) under the finite representation.
The stopping-time validity is enforced during construction.
Example
T = StoppingTime.from_values(space, values, filtration)
S = T.minimum(other)
print(S.values)