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Timeline for Convergence of random functions

Current License: CC BY-SA 4.0

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Dec 2 at 23:05 comment added Anthony Quas I’m just checking: by functional, you mean linear functional, right?
Dec 1 at 9:33 vote accept Snidd
Dec 1 at 9:32 history became hot network question
Dec 1 at 8:55 answer added Martin Hairer timeline score: 8
Dec 1 at 7:08 comment added Snidd @AnthonyQuas If F is bounded functional from $C[0,t] \to \mathbb{R}$ continuous wrt. to the topology of uniform convergence on $C[0,t]$ then it is the case that: $$\lim\limits_{n \to \infty} \mathbb{E}(F(f^{n})) = \mathbb{E}(F(f))$$
Dec 1 at 6:36 comment added Anthony Quas What does it mean to say $f^n$ converges in distribution to $f$?
Dec 1 at 0:22 history edited Snidd CC BY-SA 4.0
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Dec 1 at 0:15 history asked Snidd CC BY-SA 4.0