Abstract:

We outline a method of embedding patterns into the path of a two-sided Brownian motion. The patterns can for instance be a given distribution (the Skorokhod embedding), a particular type of excursion, or the Brownian bridge. The method is unbiased which means that conditionally on the pattern the one-sided processes developing backward and forward from the pattern are independent Brownian motions. The method relies on finding appropriate local times for the pattern. We expect the method to work also for embedding patterns in planar and spatial Brownian motion.