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Zbl 0615.01012
Bouleau, N.
La jonction entre la théorie du potentiel et les probabilités. (The junction of potential theory and probability theory). (French)
[J] Cah. Sémin. Hist. Math. 8, 43-66 (1987).

The historical development of classical potential theory since I. Newton (1685) and the history of Markov processes are described. The junction of these two theories and the correspondence of certain martingales and of certain harmonic functions is shown by the theorem of S. Kakutani (1944). Reflections are made on the existence and the nature of dictionaries $(=correspondences$ between classical potential theory, Markov processes, and martingales) which are to be found in C. Dellacherie and P.-A. Meyer (1980) and in H. Bauer (1969). It is shown that these dictionaries should be used with precaution regarding different situations and conditions, specification of hypotheses ect., and knowledge of the historical development is necessary.
[H.Grimm]

MSC 2000:: *01A65 Development of contemporary mathematics
31-03 Historical (potential theory)
60-03 Historical (probability theory)

Keywords: potential theory; Markov process; martingales; theorem of Kakutani; dictionary

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