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Proceedings of the American Mathematical Society

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Minimal coefficients in Hölder conditions in the Wiener space


Author: J. Yeh
Journal: Proc. Amer. Math. Soc. 25 (1970), 385-390
MSC: Primary 28.46
DOI: https://doi.org/10.1090/S0002-9939-1970-0255762-4
MathSciNet review: 0255762
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Abstract: For almost every $ x$ in the Wiener space $ {C_w}$, the Hölder condition $ \vert x(t') - x(t'')\vert \leqq h\vert t' - t''{\vert^\alpha }$ holds for some $ h > 0$ when $ \alpha \in (0,\tfrac{1} {2})$. Let $ {\phi _\alpha }[x]$ be the infimum of all $ h > 0$ for fixed $ x$ and $ \alpha $. In the present paper we prove that every positive power of $ {\phi _\alpha }[x]$ is Wiener integrable over $ {C_w}$ and give an estimate for the Wiener integral.


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  • [3] J. Yeh, Wiener measure in a space of functions of two variables, Trans. Amer. Math. Soc. 95 (1960), 433-450. MR 23 #A2735. MR 0125433 (23:A2735)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0255762-4
Keywords: Wiener measure, Brownian motion, continuity of sample paths, Hölder condition, essential boundedness
Article copyright: © Copyright 1970 American Mathematical Society

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