A new relation between diffusions and superdiffusions with applications to the equation lu=u
Eugene B. Dynkin · Comptes Rendus de l Académie des Sciences - Series I - Mathematics · 1997
Abstract We establish a relation between a diffusion ξ and the superdiffusion X corresponding to the spatial motion ξ and branching parameter α. It involves, on one hand, the range R and linear additive functionals of X and, on the other hand, h -transforms of process ξ. By using this relation, we investigate boundary singularities of solutions of the semilinear partial differential equation Lu=u α .