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Results tagged with martingales
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user 9564
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Brownian motion, martingales, Markov Chains - Rosetta Stone
If X is a continuous martingale of finite variation such that $X_0 = 0$, then $P(X_t = 0 \ \ \forall t) = 1$.
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Brownian motion, martingales, Markov Chains - Rosetta Stone
Levy's characterisation of Brownian motion:
If $X$ is a continuous martingale and $X$ has quadratic variation process $[ X ]_t = t$ then $X$ is a standard Brownian motion.