StoppedProcess

StoppedProcess represents the discrete process stopped at a stopping time \(T\):

\[X_n^T=X_{n\wedge T}.\]

Constructor

StoppedProcess(process, stopping_time)

Properties

Property Meaning
process Original process.
stopping_time Stopping time used for the construction.
n_steps Number of represented time levels.

Methods

  • values(n) — obtain the stopped value sequence through time n.
  • sequence() — return the stopped process sequence.
  • terminal_value() — return the terminal stopped value.

Example

M = Martingale(process, filtration)
T = StoppingTime(values, filtration)
MT = M.stopped(T)

print(MT.sequence())
print(MT.terminal_value())

Chapter 5 — Martingales à temps discret