ChatGPT and Stochastic Calculus: Martingale

Win_odd Dhamnekar

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Aug 14, 2018
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If Mn is a square integrable martingale with respect to {Fn}\{\mathcal{F}_n\} and Mn=max{M0,...,Mn}\overline{M}_n =max\{|M_0|,..., |M_n|\}
then show that for every a > 0, P{Mna}a2E[Mn2]\mathbb{P} \{\overline{M}_n \geq a \} \leq a^{-2} \mathbb{E}[M^2_n]
ChatGPT gave me the following answer:
1677002138310.png


In my opinion, It is correct.
 
In my opinion, [ChatGPT] is correct.
Hi DW. You were not surprised by that, I presume.

That particular approach could occur many times, in the "vast public corpus of human-generated text" accessed by ChatGPT (for modeling responses).

Try asking whether it had copied that response verbatim from somebody else's work. ;)
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