Additive Functionals of Superdiffusion Processes
Eugene B. Dynkin · Birkhäuser Boston eBooks · 1991
To every elliptic differential operator L in ℝ d (with time dependent coefficients) and to every 1 < α ≤ 2 there corresponds a (non homogeneous) measure-valued Markov process X which we call the superdiffusion with parameters (L, α). A class S α of “exceptional sets” in ℝ d +1 is introduced and an additive functional I η of X is constructed for every finite measure η which does not charge any set of class S α . The construction is based on a relationship between superdiffusions and a class of nonlinear parabolic partial differential equations and on results of Baras and Pierre about these equations.