summaryrefslogtreecommitdiff
path: root/content/know/concept/ito-integral/index.pdc
diff options
context:
space:
mode:
authorPrefetch2021-11-07 19:34:18 +0100
committerPrefetch2021-11-07 19:34:18 +0100
commit62759ea3f910fae2617d033bf8f878d7574f4edd (patch)
treeb958409ec1870e916e6f3a2ca91fc1aae4e1f3c5 /content/know/concept/ito-integral/index.pdc
parentf091bf0922c26238d16bf175a8ea916a16d11fba (diff)
Expand knowledge base, reorganize measure theory, update gitignore
Diffstat (limited to 'content/know/concept/ito-integral/index.pdc')
-rw-r--r--content/know/concept/ito-integral/index.pdc7
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 $B_t$.