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Proceedings of the American Mathematical Society

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A singular stochastic integral equation

Authors: David Nualart and Marta Sanz
Journal: Proc. Amer. Math. Soc. 86 (1982), 139-142
MSC: Primary 60H20; Secondary 60H05
MathSciNet review: 663883
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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.

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  • [2] R. K. Getoor and M. J. Sharpe, Conformal martingales, Invent. Math. 16 (1972), 271–308. MR 0305473
  • [3] H. P. McKean Jr., The Bessel motion and a singular integral equation, Mem. Coll. Sci. Univ. Kyoto. Ser. A Math. 33 (1960/1961), 317–322. MR 0133660
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Keywords: Stochastic integral, stochastic differential equations, (local) martingale
Article copyright: © Copyright 1982 American Mathematical Society