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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A singular stochastic integral equation
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by David Nualart and Marta Sanz PDF
Proc. Amer. Math. Soc. 86 (1982), 139-142 Request permission

Abstract:

This note is devoted to the discussion of the stochastic differential equation $XdX + YdY = 0$, $X$ and $Y$ being continuous local martingales. A method to construct solutions of this equation is given.
References
  • M. T. Barlow and M. Yor, Sur la construction d’une martingale continue, de valeur absolue donnée, Seminar on Probability, XIV (Paris, 1978/1979) Lecture Notes in Math., vol. 784, Springer, Berlin, 1980, pp. 62–75 (French). MR 580109
  • R. K. Getoor and M. J. Sharpe, Conformal martingales, Invent. Math. 16 (1972), 271–308. MR 305473, DOI 10.1007/BF01425714
  • H. P. McKean Jr., The Bessel motion and a singular integral equation, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 33 (1960/61), 317–322. MR 133660, DOI 10.1215/kjm/1250775917
  • D. Nualart, Martingales à variation indépendante du chemin, Two-index random processes (Paris, 1980) Lecture Notes in Math., vol. 863, Springer, Berlin, 1981, pp. 128–148 (French). MR 630310
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 86 (1982), 139-142
  • MSC: Primary 60H20; Secondary 60H05
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0663883-5
  • MathSciNet review: 663883