From c0d352dd0f66b47ee91fb96eaf320f895fa78790 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sun, 14 Nov 2021 17:54:04 +0100
Subject: Expand knowledge base

---
 content/know/concept/ito-calculus/index.pdc | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

(limited to 'content/know/concept/ito-calculus')

diff --git a/content/know/concept/ito-calculus/index.pdc b/content/know/concept/ito-calculus/index.pdc
index 3527b1d..7a80e2f 100644
--- a/content/know/concept/ito-calculus/index.pdc
+++ b/content/know/concept/ito-calculus/index.pdc
@@ -60,6 +60,9 @@ $$\begin{aligned}
 An Itō process $X_t$ is said to satisfy this equation
 if $f(X_t, t) = F_t$ and $g(X_t, t) = G_t$,
 in which case $X_t$ is also called an **Itō diffusion**.
+All Itō diffusions are [Markov processes](/know/concept/markov-process/),
+since only the current value of $X_t$ determines the future,
+and $B_t$ is also a Markov process.
 
 
 ## Itō's lemma
@@ -80,7 +83,7 @@ known as **Itō's lemma**:
 $$\begin{aligned}
     \boxed{
         \dd{Y_t}
-        = \pdv{h}{t} \dd{t} + \bigg( \pdv{h}{x} F_t + \frac{1}{2} G_t^2 \pdv[2]{h}{x} \bigg) \dd{t} + \pdv{h}{x} G_t \dd{B_t}
+        = \bigg( \pdv{h}{t} + \pdv{h}{x} F_t + \frac{1}{2} \pdv[2]{h}{x} G_t^2 \bigg) \dd{t} + \pdv{h}{x} G_t \dd{B_t}
     }
 \end{aligned}$$
 
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