The Annals of Probability

Nondifferentiability of curves on the Brownian sheet

Robert C. Dalang and T. Mountford

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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

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

First available in Project Euclid: 15 January 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Brownian sheet level sets nondifferentiability Jordan arc


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.

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