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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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$L^ p$ inequalities for stopping times of diffusions
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by R. Dante DeBlassie PDF
Trans. Amer. Math. Soc. 295 (1986), 765-782 Request permission

Abstract:

Let ${X_t}$ be a solution to a stochastic differential equation. Easily verified conditions on the coefficients of the equation give ${L^p}$ inequalities for stopping times of ${X_t}$ and the maximal function. An application to Brownian motion with radial drift is also discussed.
References
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  • D. L. Burkholder and R. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), 249–304. MR 440695, DOI 10.1007/BF02394573
  • Avner Friedman, Stochastic differential equations and applications. Vol. 1, Probability and Mathematical Statistics, Vol. 28, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0494490
  • Carl Mueller, Exit times of diffusions, Martingale theory in harmonic analysis and Banach spaces (Cleveland, Ohio, 1981) Lecture Notes in Math., vol. 939, Springer, Berlin-New York, 1982, pp. 98–105. MR 668540
  • Daniel W. Stroock and S. R. Srinivasa Varadhan, Multidimensional diffusion processes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 233, Springer-Verlag, Berlin-New York, 1979. MR 532498
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 295 (1986), 765-782
  • MSC: Primary 60G40; Secondary 60H10, 60J60
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0833708-1
  • MathSciNet review: 833708