Conditioned Wiener processes as nonlinearities: A rigorous probabilistic analysis of dynamics

We study a Wiener process that is conditioned to pass through finite set of points and consider the dynamics generated by iterating sample path from this process. Using topological techniques we are able characterize global deduce existence, structure approximate location invariant sets. Most importantly, compute probability characterization correct. This work probabilistic in nature intended provide theoretical foundation for statistical analysis dynamical systems which can only be queried via samples.