Set-Valued Stochastic Lebesque Integral and Representation Theorems

Set-Valued Stochastic Lebesgue Integral And Representation Theorems

In this paper, we shall firstly illustrate why we should introduce set-valued stochastic integrals, and then we shall discuss some properties of set-valued stochastic processes and the relation between a set-valued stochastic process and its selection set. After recalling the Aumann type definition of stochastic integral, we shall introduce a new definition of Lebesgue integral of a set-valued ...

Fuzzy set-valued stochastic Lebesgue integral

This paper studies Lebesgue integral of a fuzzy closed set-valued stochastic process with respect to the time t. Firstly, a progressively measurable fuzzy closed set-valued stochastic process is discussed and an almost everywhere problem in the former Aumann type Lebesgue integral of the level-set process is pointed out. Secondly, a new definition of the Lebesgue integral by decomposable closur...

Aumann Type Set-valued Lebesgue Integral and Representation Theorem

In this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact subset of d-dimensional Euclidean space. After recalling some basic results about set-valued stochastic processes, we shall secondly prove that the...

Fixed Point Theorems For Set-Valued Maps

Preface In this thesis we provide an introduction to fixed point theory for set-valued maps. It is not our goal in the present work to give an outline of the status quo of fixed point theory with all its newest achievements, but rather to give a thorough overview of the basic results in this discipline. It then should be possible for the reader to better and easier understand the newest develop...

Fixed Point Theorems for Set-valued Mappings