Filtration

Filtration represents an increasing sequence of finite partitions

\[\mathcal F_0\subseteq\mathcal F_1\subseteq\cdots,\]

used to encode the information available to a discrete-time process.

Constructor

Filtration(partitions)

Parameters

Parameter Description
partitions Ordered sequence of finite Partition objects.

Properties

Property Meaning
partitions Ordered finite partitions.
n_steps Number of filtration levels.

Class methods

  • natural(process) — construct the natural filtration generated by a finite sequence of random variables.

Methods

  • at(n) — return \(\mathcal F_n\).
  • is_adapted(process) — check whether a process is adapted to the filtration.

Example

filtration = Filtration([F0, F1, F2])
print(filtration.at(1))
print(filtration.n_steps)

Chapter 5 — Martingales à temps discret