Biographical Memoirs Volume 80 (2001) / Chapter Skim
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Edward James McShane
Edward James McShane
Pages 226-239
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BERKOVITZ AND WENDELL H FLEMING DWRING HIS KONG CAREER Edward James McShane made significant contributions to the calculus of variations, integration theory, stochastic calculus, en cl exterior ballistics.
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there for the rest of his career, except for leaves of absence spent at other institutions. With the onset of WorIcl War II McShane agreed to heacl a mathematics group at the Ballistics Research Laboratory in Aberdeen, MarylancI.
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Victor Klee, recalling his experience as a graduate student at Virginia from 1945 to 1949, wrote: "He McShane was very popular with the graduate students because of his clear lectures, his amusing anecdotes, en cl unusual kinkiness." Klee went on to tell how McShane turned his office over to the graduate students, who hac! no offices of their own: "His generosity contr~outect a lot to tne quality ot tne graduate program by providing a place for the graduate students to meet with each other en c!
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an elegant solution for geometric variational integrancis that clo not vary spatially. The key iclea was that it suffices to final the minimum in the smaller class of "sacicIle surfaces," which are representable parametrically by a vector function monotone in Lebesgue's sense.
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Another hotly of work, which was clefinitive for problems in the calculus of variations in one inclepenclent variable, was the series of three papers that appeared in 1940 in volumes six en c! seven of the Duke Mathematics journal.
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stochastic calculus. This is seen, for example, in his excellent Bulletin of the American Mathematical Society survey article "Integrals Designed for Special Purposes" (1963)
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in English. The 1953 monograph, Order Preserving Maps and Integration Processes, was an outgrowth of his search for a mathematically correct setting in which to treat divergent integrals in quantum physics.
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McShane's approach provided a particularly satisfying resolution of this issue. His stochastic integral has an important consistency property that ensures that solutions of clifferential equations representing physical systems driven by wicle-bancl noises tend in the white noise limit to the solution of the corresponding McShane-sense stochastic clifferential equation.
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We also wish to thank McShane's family and Victor Klee for many helpful suggestions and for their warm encouragement.
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Princeton, N.J.: Princeton University Press. 1950 The differentials of certain functions in exterior ballistics.
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New York: Academic Press. 1975 Stochastic differential equations.
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1983 Unified Integration. New York: Academic Press.
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