Stability of a class of transformations of distribution-valued processes and stochastic evolution equations
Since 1976, many results on convergence of the processes taking values in distribution spaces have been proven. The processes and their limits are often solutions of stochastic evolution equations involving accompanying semimartingales and therefore the question can be posed as a problem of convergence of solutions to such equations and relationships between convergence of solutions and convergence of accompanying semimartingales. This problem belongs to a more general question of stability of a class of linear transformations of processes. This general question is studied and the results are translated into theorems on stochastic evolution equations. Two general results (Theorems 4 and 5) on convergence of solutions of stochastic evolution equations in distribution spaces which cover a large class of applications are given. In these results the distribution spaces are duals of Fréchet nuclear spaces. One of the results, for the case of continuous limits, considerably simplifies the tightness problem due to a recent result of Aldous (Theorem 5).
relationships between convergence of solutions and convergence of accompanying semimartingales
stability of a class of linear transformations of processes
scientific article; zbMATH DE number 96936
scientific article