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.
Citation
Robert C. Dalang. T. Mountford. "Nondifferentiability of curves on the Brownian sheet." Ann. Probab. 24 (1) 182 - 195, January 1996. https://doi.org/10.1214/aop/1042644712
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