Some problems on super-diffusions and one class of nonlinear differential equations

摘要

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 he domains enlarge to the whole space. As an important application of superproocess, the representation of solutions of involved differential equations is used in term of historical sueprprocesses. 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.