We study certain singularities of the Brownian sheet which have the property that they propagate parallel to the coordinate axis. This is used to give an intuitive explanation of the fact that the Brownian sheet does not satisfy Levy's sharp Markov property.
"Propagation of Singularities in the Brownian Sheet." Ann. Probab. 10 (2) 279 - 288, May, 1982. https://doi.org/10.1214/aop/1176993857