Abstract: This paper discusses the property of semimartingales of B-valued R. R. C. process W, and the relation between this property and critical stopping time σ_ẇ of W after giving the definition of σ_ẇ and the structural approach to σ_ẇ. A conclusion is drawn from this paper that the process W being a non-semimartingale is characterized by P(σ_ẇ<∞) > 0.
Finally, two kinds of vector valued processes with R-control process are discussed, and they are shown to be non-semimartingales by the use of Theorem 2 in this paper.