Type: Article
Publication Date: 2023-05-07
Citations: 2
DOI: https://doi.org/10.1007/s00208-023-02613-x
Abstract Following our previous work on complementary boundary conditions, we write Cartesian product of two copies of a space of continuous functions on the real line as the direct sum of two subspaces that are invariant under a cosine family of operators underlying Brownian motion. Both these subspaces are formed by pairs of extensions of continuous functions: in the first subspace the form of these extensions is shaped unequivocally by the transmission conditions describing snapping out Brownian motion, in the second, it is shaped by the transmission conditions of skew Brownian motion with certain degree of stickiness. In this sense, the above transmission conditions are complementary to each other.