Investigations in the theory of Markov processes are to be done with concentration on branching measure-valued processes and related processes in spaces of functions. The general form of branching, the relationship between path properties of superdiffusions and positive solutions of nonlinear differential equations and modeling of "a random cloud" with interacting parts are among the principal objectives of the investigation. Measure-valued branching processes have been studied since the late 1960s and have attracted a great deal of attention during the last five years. This is a remarkable class of processes, which provide a tool for the investigation of spatially distributed populations. They also make it possible to extend important connections between probability theory and the theory of partial differential equations.
