Lebesgues-Stieltjes Integrals of Fuzzy Stochastic Processes with Respect to Finite Variation Processes

Jinping Zhang, Lingli Luo, Xingmei Li, Xiaoying Wang

Department of Mathematics and Physics, North China Electric Power University, Beijing, China.

DOI: 10.4236/am.2015.613193                

Abstract

Let be a fuzzy stochastic process and be a real valued finite variation process. We define the Lebesgue-Stieltjes integral denoted by for each by using the selection method, which is direct, nature and different from the indirect definition appearing in some references. We shall show that this kind of integral is also measurable, continuous in time t and bounded a.s. under the Hausdorff metric.

Keywords

Fuzzy Stochastic Process, Finite Variation Process, Fuzzy Stochastic Lebesgue-Stieltjes Integral, Measurability

Conflicts of Interest

The authors declare no conflicts of interest.

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