ChatGPT and Stochastic Calculus: Martingale

[Win_odd Dhamnekar]

If Mn is a square integrable martingale with respect to [imath]\{\mathcal{F}_n\}[/imath] and [math]\overline{M}_n =max\{|M_0|,..., |M_n|\}[/math]
then show that for every a > 0, [math]\mathbb{P} \{\overline{M}_n \geq a \} \leq a^{-2} \mathbb{E}[M^2_n][/math]
ChatGPT gave me the following answer:



In my opinion, It is correct.

 

[Otis]

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.
[imath]\;[/imath]