Right continuous fuzzy set-valued stochastic processes with left limitation

Abstract

The concept of (d) quasi-left continuous fuzzy set-valued stochastic process is proposed. A (d) cadlag. fuzzy set-valued stochastic process, i.e. (d) right continuous fuzzy set-valued stochastic processes with left limitation, is (d) quasi-left continuous if and only if for each positive predictable time this process is (d) left continuous almost surely on the set on which the predictable time is finite. A (d) cadlag. fuzzy set-valued stochastic process only has accessible jump if and only if for each totally inaccessible time this process is (d) left continuous almost surely on the set on which the totally inaccessible time is finite.