The Annals of Probability

Nondifferentiability of curves on the Brownian sheet

Robert C. Dalang and T. Mountford

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Abstract

For a Brownian sheet on the nonnegative quadrant, we show that any nontrivial curve in the quadrant with the property that the Brownian sheet restricted to the curve gives rise to a differentiable function cannot be differentiable at any point. This result has several implications for level sets of the Brownian sheet. In particular, any Jordan arc contained in a level set must be nowhere differentiable.

Article information

Source
Ann. Probab., Volume 24, Number 1 (1996), 182-195.

Dates
First available in Project Euclid: 15 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1042644712

Digital Object Identifier
doi:10.1214/aop/1042644712

Mathematical Reviews number (MathSciNet)
MR1387631

Zentralblatt MATH identifier
0861.60058

Subjects
Primary: 60G60: Random fields
Secondary: 60G15: Gaussian processes

Keywords
Brownian sheet level sets nondifferentiability Jordan arc

Citation

Dalang, Robert C.; Mountford, T. Nondifferentiability of curves on the Brownian sheet. Ann. Probab. 24 (1996), no. 1, 182--195. doi:10.1214/aop/1042644712. https://projecteuclid.org/euclid.aop/1042644712


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