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/martingale/index.pdc | 8 ++++++++
 1 file changed, 8 insertions(+)

(limited to 'content/know/concept/martingale/index.pdc')

diff --git a/content/know/concept/martingale/index.pdc b/content/know/concept/martingale/index.pdc
index 21fa918..41c2709 100644
--- a/content/know/concept/martingale/index.pdc
+++ b/content/know/concept/martingale/index.pdc
@@ -37,6 +37,14 @@ Accordingly, the [Wiener process](/know/concept/wiener-process/) $B_t$
 (Brownian motion) is an example of a martingale,
 since each of its increments $B_t \!-\! B_s$ has mean $0$ by definition.
 
+Martingales are easily confused with
+[Markov processes](/know/concept/markov-process/),
+because stochastic processes will often be both,
+e.g. the Wiener process.
+However, these are distinct concepts:
+the martingale property says nothing about history-dependence,
+and the Markov property does not say *what* the future expectation should be.
+
 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:
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