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-rw-r--r--source/know/concept/martingale/index.md6
1 files changed, 4 insertions, 2 deletions
diff --git a/source/know/concept/martingale/index.md b/source/know/concept/martingale/index.md
index 9d3c6b4..53a346a 100644
--- a/source/know/concept/martingale/index.md
+++ b/source/know/concept/martingale/index.md
@@ -45,12 +45,14 @@ Modifying property (3) leads to two common generalizations.
The stochastic process $$M_t$$ above is a **submartingale**
if the current value is a lower bound for the expectation:
-3. For $$0 \le s \le t$$, the conditional expectation $$\mathbf{E}(M_t | \mathcal{F}_s) \ge M_s$$.
+3. For $$0 \le s \le t$$, the conditional expectation
+ $$\mathbf{E}(M_t | \mathcal{F}_s) \ge M_s$$.
Analogouly, $$M_t$$ is a **supermartingale**
if the current value is an upper bound instead:
-3. For $$0 \le s \le t$$, the conditional expectation $$\mathbf{E}(M_t | \mathcal{F}_s) \le M_s$$.
+3. For $$0 \le s \le t$$, the conditional expectation
+ $$\mathbf{E}(M_t | \mathcal{F}_s) \le M_s$$.
Clearly, submartingales and supermartingales are *biased* random walks,
since they will tend to increase and decrease with time, respectively.