diff options
Diffstat (limited to 'content/know/concept/ito-integral/index.pdc')
| -rw-r--r-- | content/know/concept/ito-integral/index.pdc | 7 |
1 files changed, 3 insertions, 4 deletions
diff --git a/content/know/concept/ito-integral/index.pdc b/content/know/concept/ito-integral/index.pdc index ec49189..cbd4a91 100644 --- a/content/know/concept/ito-integral/index.pdc +++ b/content/know/concept/ito-integral/index.pdc @@ -13,9 +13,8 @@ markup: pandoc # Itō integral The **Itō integral** offers a way to integrate -a time-indexed [random variable](/know/concept/random-variable/) -$G_t$ (i.e. a stochastic process) with respect -to a [Wiener process](/know/concept/wiener-process/) $B_t$, +a given [stochastic process](/know/concept/stochastic-process/) $G_t$ +with respect to a [Wiener process](/know/concept/wiener-process/) $B_t$, which is also a stochastic process. The Itō integral $I_t$ of $G_t$ is defined as follows: @@ -29,7 +28,7 @@ $$\begin{aligned} Where have partitioned the time interval $[a, b]$ into steps of size $h$. The above integral exists if $G_t$ and $B_t$ are adapted -to a common [filtration](/know/concept/sigma-algebra) $\mathcal{F}_t$, +to a common filtration $\mathcal{F}_t$, and $\mathbf{E}[G_t^2]$ is integrable for $t \in [a, b]$. If $I_t$ exists, $G_t$ is said to be **Itō-integrable** with respect to $B_t$. |