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authorPrefetch2021-11-14 17:54:04 +0100
committerPrefetch2021-11-14 17:54:04 +0100
commitc0d352dd0f66b47ee91fb96eaf320f895fa78790 (patch)
tree961eb3f1c6afcd418b0319aa2ec4c2c51b84f92a /content/know/concept/ito-calculus
parentf2970c55894b3c8d5fd2926a8918d166988109fe (diff)
Expand knowledge base
Diffstat (limited to 'content/know/concept/ito-calculus')
-rw-r--r--content/know/concept/ito-calculus/index.pdc5
1 files changed, 4 insertions, 1 deletions
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}$$