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)