S~*(M)-valued Measure And Related Problems

Discrete-time normal martingales are important stochastic processes in proba-bility theory,and their functionals have attracted more and more attention in recent years.In this paper,we focus on developing the integration of S~*(M)-valued mea-sures and S~*(M)-valued functions,where S~*(M)means the generalized functional space of a discrete-time normal martingale M.The main work is as followsFirstly,the concept of an S~*(M)-valued measure is defined.Based on this,we deeply investigate the properties of S~*(M)-valued measures by their Fock transforms,and obtain the appropriate conditions for this kind of measures to be countably additive in normSecondly,we mainly discuss the integral of an S~*(M)-valued function with respect to a scalar-valued measure and its propertiesFinally,we introduce the Bochner-Wick integral of an S~*(M)-valued function with respect to an S~*(M)-valued measure,prove a corresponding theorem of in-tegrability,and establish a corresponding dominated convergence theorem.Some other results are also obtained.