5 Brownian motion as a martingale
Let I be some subset of [0, ∞] and 
a filtration, i. e. an increasing family of sub-σ-algebras of 
. Recall that a martingale 
is a real or complex stochastic process 
or 
satisfying
- a) for all t ∊ I;
- b) Xt is ℱt
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