# Category:Adapted Stochastic Processes

This category contains results about **adapted stochastic processes**.

### Discrete Time

Let $\struct {\Omega, \Sigma, \sequence {\FF_n}_{n \mathop \in \N}, \Pr}$ be a filtered probability space.

Let $\sequence {X_n}_{n \mathop \in \N}$ be a sequence of real-valued random variables.

We say that $\sequence {X_n}_{n \mathop \in \N}$ is an **adapted stochastic process** if and only if:

- $X_n$ is $\FF_n$-measurable random variable for each $n \in \N$.

### Continuous Time

Let $\struct {\Omega, \Sigma, \sequence {\FF_t}_{t \ge 0}, \Pr}$ be a filtered probability space.

Let $\sequence {X_t}_{t \ge 0}$ be a $\hointr 0 \infty$-indexed family of real-valued random variables.

We say that $\sequence {X_t}_{t \ge 0}$ is an **adapted stochastic process** if and only if:

- $X_t$ is $\FF_t$-measurable for each $t \in \hointr 0 \infty$.

## Subcategories

This category has the following 6 subcategories, out of 6 total.

### D

### M

### S

## Pages in category "Adapted Stochastic Processes"

The following 5 pages are in this category, out of 5 total.