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diff --git a/source/know/concept/ito-integral/index.md b/source/know/concept/ito-integral/index.md
index 3f17a9a..f087f97 100644
--- a/source/know/concept/ito-integral/index.md
+++ b/source/know/concept/ito-integral/index.md
@@ -9,10 +9,10 @@ layout: "concept"
 ---
 
 The **Itō integral** offers a way to integrate
-a given [stochastic process](/know/concept/stochastic-process/) $G_t$
-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:
+The Itō integral $$I_t$$ of $$G_t$$ is defined as follows:
 
 $$\begin{aligned}
     \boxed{
@@ -22,17 +22,17 @@ $$\begin{aligned}
     }
 \end{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 $\mathcal{F}_t$,
-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 $B_t$.
+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 $$\mathcal{F}_t$$,
+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 $$B_t$$.
 
 
 ## Motivation
 
-Consider the following simple first-order differential equation for $X_t$,
-for some function $f$:
+Consider the following simple first-order differential equation for $$X_t$$,
+for some function $$f$$:
 
 $$\begin{aligned}
     \dv{X_t}{t}
@@ -40,7 +40,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 This can be solved numerically using the explicit Euler scheme
-by discretizing it with step size $h$,
+by discretizing it with step size $$h$$,
 which can be applied recursively, leading to:
 
 $$\begin{aligned}
@@ -51,7 +51,7 @@ $$\begin{aligned}
     \approx X_0 + \sum_{s = 0}^{s = t} f(X_s) \: h
 \end{aligned}$$
 
-In the limit $h \to 0$, this leads to the following unsurprising integral for $X_t$:
+In the limit $$h \to 0$$, this leads to the following unsurprising integral for $$X_t$$:
 
 $$\begin{aligned}
     \int_0^t f(X_s) \dd{s}
@@ -59,18 +59,18 @@ $$\begin{aligned}
 \end{aligned}$$
 
 In contrast, consider the *stochastic differential equation* below,
-where $\xi_t$ represents white noise,
-which is informally the $t$-derivative
-of the Wiener process $\xi_t = \idv{B_t}{t}$:
+where $$\xi_t$$ represents white noise,
+which is informally the $$t$$-derivative
+of the Wiener process $$\xi_t = \idv{B_t}{t}$$:
 
 $$\begin{aligned}
     \dv{X_t}{t}
     = g(X_t) \: \xi_t
 \end{aligned}$$
 
-Now $X_t$ is not deterministic,
-since $\xi_t$ is derived from a random variable $B_t$.
-If $g = 1$, we expect $X_t = X_0 + B_t$.
+Now $$X_t$$ is not deterministic,
+since $$\xi_t$$ is derived from a random variable $$B_t$$.
+If $$g = 1$$, we expect $$X_t = X_0 + B_t$$.
 With this in mind, we introduce the **Euler-Maruyama scheme**:
 
 $$\begin{aligned}
@@ -80,7 +80,7 @@ $$\begin{aligned}
     &= X_t + g(X_t) \: (B_{t+h} - B_t)
 \end{aligned}$$
 
-We would like to turn this into an integral for $X_t$, as we did above.
+We would like to turn this into an integral for $$X_t$$, as we did above.
 Therefore, we state:
 
 $$\begin{aligned}
@@ -89,8 +89,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 This integral is *defined* as below,
-analogously to the first, but with $h$ replaced by
-the increment $B_{t+h} \!-\! B_t$ of a Wiener process.
+analogously to the first, but with $$h$$ replaced by
+the increment $$B_{t+h} \!-\! B_t$$ of a Wiener process.
 This is an Itō integral:
 
 $$\begin{aligned}
@@ -104,14 +104,14 @@ see the [Itō calculus](/know/concept/ito-calculus/).
 
 ## Properties
 
-Since $G_t$ and $B_t$ must be known (i.e. $\mathcal{F}_t$-adapted)
-in order to evaluate the Itō integral $I_t$ at any given $t$,
-it logically follows that $I_t$ is also $\mathcal{F}_t$-adapted.
+Since $$G_t$$ and $$B_t$$ must be known (i.e. $$\mathcal{F}_t$$-adapted)
+in order to evaluate the Itō integral $$I_t$$ at any given $$t$$,
+it logically follows that $$I_t$$ is also $$\mathcal{F}_t$$-adapted.
 
 Because the Itō integral is defined as the limit of a sum of linear terms,
 it inherits this linearity.
-Consider two Itō-integrable processes $G_t$ and $H_t$,
-and two constants $v, w \in \mathbb{R}$:
+Consider two Itō-integrable processes $$G_t$$ and $$H_t$$,
+and two constants $$v, w \in \mathbb{R}$$:
 
 $$\begin{aligned}
     \int_a^b v G_t + w H_t \dd{B_t}
@@ -119,7 +119,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 By adding multiple summations,
-the Itō integral clearly satisfies, for $a < b < c$:
+the Itō integral clearly satisfies, for $$a < b < c$$:
 
 $$\begin{aligned}
     \int_a^c G_t \dd{B_t}
@@ -127,8 +127,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 A more interesting property is the **Itō isometry**,
-which expresses the expectation of the square of an Itō integral of $G_t$
-as a simpler "ordinary" integral of the expectation of $G_t^2$
+which expresses the expectation of the square of an Itō integral of $$G_t$$
+as a simpler "ordinary" integral of the expectation of $$G_t^2$$
 (which exists by the definition of Itō-integrability):
 
 $$\begin{aligned}
@@ -144,14 +144,14 @@ $$\begin{aligned}
 <div class="hidden" markdown="1">
 <label for="proof-isometry">Proof.</label>
 We write out the left-hand side of the Itō isometry,
-where eventually $h \to 0$:
+where eventually $$h \to 0$$:
 
 $$\begin{aligned}
     \mathbf{E} \bigg[ \sum_{t = a}^{t = b} G_t (B_{t + h} \!-\! B_t) \bigg]^2
     &= \sum_{t = a}^{t = b} \sum_{s = a}^{s = b} \mathbf{E} \bigg[ G_t G_s (B_{t + h} \!-\! B_t) (B_{s + h} \!-\! B_s) \bigg]
 \end{aligned}$$
 
-In the particular case $t \ge s \!+\! h$,
+In the particular case $$t \ge s \!+\! h$$,
 a given term of this summation can be rewritten
 as follows using the *law of total expectation*
 (see [conditional expectation](/know/concept/conditional-expectation/)):
@@ -161,18 +161,18 @@ $$\begin{aligned}
     = \mathbf{E} \bigg[ \mathbf{E} \Big[ G_t G_s (B_{t + h} \!-\! B_t) (B_{s + h} \!-\! B_s) \Big| \mathcal{F}_t \Big] \bigg]
 \end{aligned}$$
 
-Recall that $G_t$ and $B_t$ are adapted to $\mathcal{F}_t$:
-at time $t$, we have information $\mathcal{F}_t$,
-which includes knowledge of the realized values $G_t$ and $B_t$.
-Since $t \ge s \!+\! h$ by assumption, we can simply factor out the known quantities:
+Recall that $$G_t$$ and $$B_t$$ are adapted to $$\mathcal{F}_t$$:
+at time $$t$$, we have information $$\mathcal{F}_t$$,
+which includes knowledge of the realized values $$G_t$$ and $$B_t$$.
+Since $$t \ge s \!+\! h$$ by assumption, we can simply factor out the known quantities:
 
 $$\begin{aligned}
     \mathbf{E} \Big[ G_t G_s (B_{t + h} \!-\! B_t) (B_{s + h} \!-\! B_s) \Big]
     = \mathbf{E} \bigg[ G_t G_s (B_{s + h} \!-\! B_s) \: \mathbf{E} \Big[ (B_{t + h} \!-\! B_t) \Big| \mathcal{F}_t \Big] \bigg]
 \end{aligned}$$
 
-However, $\mathcal{F}_t$ says nothing about
-the increment $(B_{t + h} \!-\! B_t) \sim \mathcal{N}(0, h)$,
+However, $$\mathcal{F}_t$$ says nothing about
+the increment $$(B_{t + h} \!-\! B_t) \sim \mathcal{N}(0, h)$$,
 meaning that the conditional expectation is zero:
 
 $$\begin{aligned}
@@ -181,7 +181,7 @@ $$\begin{aligned}
     \qquad \mathrm{for}\; t \ge s + h
 \end{aligned}$$
 
-By swapping $s$ and $t$, the exact same result can be obtained for $s \ge t \!+\! h$:
+By swapping $$s$$ and $$t$$, the exact same result can be obtained for $$s \ge t \!+\! h$$:
 
 $$\begin{aligned}
     \mathbf{E} \Big[ G_t G_s (B_{t + h} \!-\! B_t) (B_{s + h} \!-\! B_s) \Big]
@@ -189,7 +189,7 @@ $$\begin{aligned}
     \qquad \mathrm{for}\; s \ge t + h
 \end{aligned}$$
 
-This leaves only one case which can be nonzero: $[t, t\!+\!h] = [s, s\!+\!h]$.
+This leaves only one case which can be nonzero: $$[t, t\!+\!h] = [s, s\!+\!h]$$.
 Applying the law of total expectation again yields:
 
 $$\begin{aligned}
@@ -199,8 +199,8 @@ $$\begin{aligned}
     &= \sum_{t = a}^{t = b} \mathbf{E} \bigg[ \mathbf{E} \Big[ G_t^2 (B_{t + h} \!-\! B_t)^2 \Big| \mathcal{F}_t \Big] \bigg]
 \end{aligned}$$
 
-We know $G_t$, and the expectation value of $(B_{t+h} \!-\! B_t)^2$,
-since the increment is normally distributed, is simply the variance $h$:
+We know $$G_t$$, and the expectation value of $$(B_{t+h} \!-\! B_t)^2$$,
+since the increment is normally distributed, is simply the variance $$h$$:
 
 $$\begin{aligned}
     \mathbf{E} \bigg[ \sum_{t = a}^{t = b} G_t (B_{t + h} \!-\! B_t) \bigg]^2
@@ -208,6 +208,7 @@ $$\begin{aligned}
     \longrightarrow
     \int_a^b \mathbf{E} \big[ G_t^2 \big] \dd{t}
 \end{aligned}$$
+
 </div>
 </div>
 
@@ -221,9 +222,9 @@ since true white noise cannot be biased.
 <label for="proof-martingale">Proof</label>
 <div class="hidden" markdown="1">
 <label for="proof-martingale">Proof.</label>
-We will prove that an arbitrary Itō integral $I_t$ is a martingale.
-Using additivity, we know that the increment $I_t \!-\! I_s$
-is as follows, given information $\mathcal{F}_s$:
+We will prove that an arbitrary Itō integral $$I_t$$ is a martingale.
+Using additivity, we know that the increment $$I_t \!-\! I_s$$
+is as follows, given information $$\mathcal{F}_s$$:
 
 $$\begin{aligned}
     \mathbf{E} \big[ I_t \!-\! I_s | \mathcal{F}_s \big]
@@ -232,8 +233,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 We rewrite this [conditional expectation](/know/concept/conditional-expectation/)
-using the *tower property* for some $\mathcal{F}_u \supset \mathcal{F}_s$,
-such that $G_u$ and $B_u$ are known, but $B_{u+h} \!-\! B_u$ is not:
+using the *tower property* for some $$\mathcal{F}_u \supset \mathcal{F}_s$$,
+such that $$G_u$$ and $$B_u$$ are known, but $$B_{u+h} \!-\! B_u$$ is not:
 
 $$\begin{aligned}
     \mathbf{E} \big[ I_t \!-\! I_s | \mathcal{F}_s \big]
@@ -242,7 +243,7 @@ $$\begin{aligned}
     = 0
 \end{aligned}$$
 
-We now have everything we need to calculate $\mathbf{E} [ I_t | \mathcal{F_s} ]$,
+We now have everything we need to calculate $$\mathbf{E} [ I_t | \mathcal{F_s} ]$$,
 giving the martingale property:
 
 $$\begin{aligned}
@@ -252,12 +253,12 @@ $$\begin{aligned}
     = I_s
 \end{aligned}$$
 
-For the existence of $I_t$,
-we need $\mathbf{E}[G_t^2]$ to be integrable over the target interval,
-so from the Itō isometry we have $\mathbf{E}[I]^2 < \infty$,
-and therefore $\mathbf{E}[I] < \infty$,
-so $I_t$ has all the properties of a Martingale,
-since it is trivially $\mathcal{F}_t$-adapted.
+For the existence of $$I_t$$,
+we need $$\mathbf{E}[G_t^2]$$ to be integrable over the target interval,
+so from the Itō isometry we have $$\mathbf{E}[I]^2 < \infty$$,
+and therefore $$\mathbf{E}[I] < \infty$$,
+so $$I_t$$ has all the properties of a Martingale,
+since it is trivially $$\mathcal{F}_t$$-adapted.
 </div>
 </div>