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)

Chapter 5 — Martingales à temps discret