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Diffstat (limited to 'content/know/concept/martingale/index.pdc')
| -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: |