I heard "Feller made a famous mistake in 1954 and fixed by A.D. Wentell in 1959" from one lecture. There is no further explain what is that mistake? Is there someone know it? Is it possible to explain a little bit it?
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asked May 7, 2022 at 15:11
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12$\begingroup$ Why not ask the lecturer? $\endgroup$– LSpiceCommented May 7, 2022 at 15:28
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5$\begingroup$ Biggest "mistake" by Feller (in the '60s, not in the '50s) was writing the 2nd edition of "An Introduction to Probability Theory and Its Applications, Vol 2" before writing the 1st edition of Vol3, which supposedly would have been on diffusion processes. The guy ups and dies before Vol 3 ever got written. $\endgroup$– Mark L. StoneCommented May 7, 2022 at 17:02
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$\begingroup$ It is the recording lecture. Thank you!! $\endgroup$– Fractional analysicsCommented May 7, 2022 at 18:45
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2$\begingroup$ Can you link to the lecture? $\endgroup$– Todd TrimbleCommented May 8, 2022 at 2:29
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$\begingroup$ Sorry, I tried it but it can not be linked. $\endgroup$– Fractional analysicsCommented May 8, 2022 at 17:40
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1 Answer
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For reference, the two papers are
[1] W. Feller. Diffusion processes in one dimension, Trans. Amer. Math. Soc. 97, 1-31 (1954).
[2] A. D. Wentzell. On boundary conditions for multidimensional diffusion processes, Theor. Probability Appl. 4, 164-177 (1959).
Differential operators with boundary conditions containing diffusion terms were introduced by Feller [1] for one-dimensional diffusion and by Wentzell [2] for higher dimensions.
My best guess to what is going on is that the the lecturer was referring to the limitation to one dimension in Feller's 1954 work, a limitation removed by Wentzell's 1959 paper. I am not aware of any error in [1].
answered May 7, 2022 at 15:45
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2$\begingroup$ This doesn’t answer the question; surely it’s only a comment? $\endgroup$ Commented May 7, 2022 at 17:02