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In stochastic calculus, the name Stratonovich appears all over the place. However, even though Donald Fisk supposedly obtained similar results, his name appears nowhere. Who was Donald Fisk?

I cannot find anything about him, nor why he isn't given any credit.

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    $\begingroup$ How did you come to know that Donald Fisk "supposedly obtained similar results", if "his name appears nowhere"? $\endgroup$ Oct 18 at 19:06
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    $\begingroup$ D. Fisk. Quasi-martingales and stochastic integrals. PhD Dissertation, Michigan State University, Department of Statistics, 1963. $\endgroup$ Oct 18 at 19:09
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    $\begingroup$ Search it at lib.msu.edu $\endgroup$ Oct 18 at 19:14
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He was a PhD student of Herman Rubin at the Michigan State University in the early 1960-s. Some of the history is reconstructed by Jarrow and Protter in A short history of stochastic integration and mathematical finance based on private communication with Rubin. Rubin gave Fisk the ideas to work on, and he developed them in his thesis Quasi-martingales and Stochastic Integrals. According to Rubin's interview with Bock, the thesis was written in 1961, MSU published it in 1963.

However, when the work was submitted to a journal the editor doubted utility of stochastic integration, and Fisk ultimately published only the part about quasimartingales, see Fisk, Quasi-martingales (1965) (Transactions of AMS, 120, pp. 369-389). This explains why he is not given credit as much as Stratonovich, although, technically, MSU did publish his thesis in full. Also, he quickly dropped off the mathematical grid. The only other publication by him listed on MathSciNet is Sample quadratic variation of sample continuous, second order martingales in Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1966.

Here is from Jarrow-Protter:

"At the Third Berkeley Symposium in 1955, Rubin gave a talk on stochastic differential equations. The following year, he presented an invited paper at the Seattle joint meetings of the Institute of Mathematical Statistics, the American Mathematical Society , the Biometric Society, the Mathematical Association of America, and the Econometrics Society. In this paper he outlined what was later to become D. L. Fisk’s Ph.D. thesis, which invented both quasimartingales and what is now known as the Stratonovich integral. To quote his own recollections:“...Quasimartingales seemed the natural candidate for the class of processes, but I did not see a clear proof. I gave the problem to Fisk to work on for a Ph.D. thesis, and he did come up with what was needed”.

Indeed, in D. L. Fisk’s thesis [27], written under Rubin when he was at Michigan State University, Fisk developed what is now known as the Stratonovich integral, and he also coined the phrase and developed the modern theory of quasimartingales, later used by K. M. Rao [68] to give an elegant proof that a quasimartingale is the difference of two submartingales, and also used by S. Orey [63] in a paper extending the idea and which foreshadowed modern day semimartingales. Fisk submitted his thesis for publication, but the editor did not believe there was much interest in stochastic integration, again according to the recollections of Herman Rubin [69]. So Fisk dropped that part of the thesis and did not pursue it, publishing instead only the part on quasimartingales, which appeared as [28]."

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    $\begingroup$ It looks like this is his obituary: Donald Leroy Fisk, December 12, 1937 – May 28, 2011 [...] He received his Ph.D. from Michigan State University; was a Professor of Mathematics at North Western, Kent State University and retired from Central Michigan University. Donald was the son of Toras and Edna Fisk of Alaska. $\endgroup$
    – njuffa
    Oct 19 at 8:17
  • $\begingroup$ In Michigan State University lOOth Annual Commencement, Sunday, June 12, 1960: DEGREE OF MASTER OF ARTS - Mathematics Donald LeRoy Fisk $\endgroup$
    – njuffa
    Oct 19 at 8:29
  • $\begingroup$ In U.S. Government Research Reports, Vol. 30, No. 13, July 5, 1964: "Michigan State Univ., East Lansing, QUASI-MARTINGALES AND STOCHASTIC INTEGRALS, Technical rept. no. 1, by Donald L. Fisk, 2 Aug 63, 95p Contract Nonr2587 02 AD 414 838 Unclassified report Descriptors: (*Statistical analysis, Theory), (*Integrals, Stochastic processes), (*Stochastic processes, Integrals), Measure theory, Probability, Statistical processes." $\endgroup$
    – njuffa
    Oct 19 at 8:46
  • $\begingroup$ CMU Bulletins, June 1987, p. 271: Donald L. Fisk (1969) Professor, Mathematics. B.A., M.A, Ph.D., Michigan State University $\endgroup$
    – njuffa
    Oct 19 at 9:11
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    $\begingroup$ A scan of Fisk's 95-page technical report "Quasi-Martingales and Stochastic Integrals", dated August 2, 1963 is available from DTIC $\endgroup$
    – njuffa
    Oct 19 at 9:35

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