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author | Prefetch | 2021-11-14 17:54:04 +0100 |
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committer | Prefetch | 2021-11-14 17:54:04 +0100 |
commit | c0d352dd0f66b47ee91fb96eaf320f895fa78790 (patch) | |
tree | 961eb3f1c6afcd418b0319aa2ec4c2c51b84f92a /content/know/concept/martingale | |
parent | f2970c55894b3c8d5fd2926a8918d166988109fe (diff) |
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Diffstat (limited to 'content/know/concept/martingale')
-rw-r--r-- | content/know/concept/martingale/index.pdc | 8 |
1 files changed, 8 insertions, 0 deletions
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: |