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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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Space-time processes, parabolic functions and one-dimensional diffusions
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by Tze Leung Lai PDF
Trans. Amer. Math. Soc. 175 (1973), 409-438 Request permission

Abstract:

In this paper, we study the properties of the space-time process and of parabolic functions associated with a Markov process. Making use of these properties and the asymptotic behavior of the first passage probabilities near the boundary points, we prove certain theorems concerning when $u(X(t),t)$ is a martingale, where $X(t)$ is a conservative regular one-dimensional diffusion with inaccessible boundaries. A characterization of the class of parabolic functions associated with classical diffusions is also obtained.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 175 (1973), 409-438
  • MSC: Primary 60J60
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0334337-X
  • MathSciNet review: 0334337