The historical superprocesses are considered on bounded regular domains with a complete branching form, as a probabilistic argument, the limit property of superprocesses is studied when the domains enlarge to the whole space. As an important application of superprocess, the representation of solutions of involved differential equations is used in term of historical superprocesses. The differential equations including the existence of nonnegative solution, the closeness of solutions and probabilistic representations to the maximal and minimal solutions are discussed, which helps develop the well-known results on nonlinear differential equations.
Evans, S. N., O’connell, N., Weighted occupation times for branching particle systems and a representation for the supercritical superprocess,Canad. Math. Bull., 1994, 37(2): 187.MATHMathSciNetGoogle Scholar