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Lebesgues-Stieltjes Integrals of Fuzzy Stochastic Processes with Respect to Finite Variation Processes
Department of Mathematics and Physics, North China Electric Power University, Beijing, China
Department of Mathematics and Physics, North China Electric Power University, Beijing, China
Department of Mathematics and Physics, North China Electric Power University, Beijing, China
Department of Mathematics and Physics, North China Electric Power University, Beijing, China
- 1 Department of Mathematics and Physics, North China Electric Power University, Beijing, China
- 2 Department of Mathematics and Physics, North China Electric Power University, Beijing, China
- 3 Department of Mathematics and Physics, North China Electric Power University, Beijing, China
- 4 Department of Mathematics and Physics, North China Electric Power University, Beijing, China
Applied Mathematics·Volume 06 (2015)·Pages 2199–2210·Published 30 November 2015·DOI10.4236/am.2015.613193
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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.
KeywordsFuzzy Stochastic ProcessFinite Variation ProcessFuzzy Stochastic Lebesgue-Stieltjes IntegralMeasurability
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