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Results tagged with martingales
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user 15570
1
vote
Weaker version of the martingale convergence theorem
Let $\Omega=\{-1,1\} \times \{-1,1\}$ with the discrete $\sigma$-algebra and uniform measure, let $X(\omega_1,\omega_2)=\omega_2$, and let
$$ \mathcal{A}_n \ = \ \left\{ \begin{array}{l l} \sigma(\{\o …
- 708
3
votes
0
answers
108
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Has there been any study of the "extreme convergence property" for martingales?
. $$
My vauge intuition is that most uniformly bounded martingales arising in practice will have the extreme convergence property, or at least the extreme-convergence decomposability property … outside a random repelling singleton; and even when the stochastic flow does not have this behaviour, I believe that typically the above martingale can be expressed as an equal-weight convex combination of martingales …
- 708