Fuzzy Stochastic Differential Equations Driven by Semimartingales-Different Approaches
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-01-12
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
The first aim of the paper is to present a survey of possible approaches for the study of fuzzy stochastic differential or integral equations.
They are stochastic counterparts of classical approaches known from the theory of deterministic fuzzy differential equations.
For our aims we present first a notion of fuzzy stochastic integral with a semimartingale integrator and its main properties.
Next we focus on different approaches for fuzzy stochastic differential equations.
We present the existence of fuzzy solutions to such equations as well as their main properties.
In the first approach we treat the fuzzy equation as an abstract relation in the metric space of fuzzy sets over the space of square integrable random vectors.
In the second one the equation is interpreted as a system of stochastic inclusions.
Finally, in the last section we discuss fuzzy stochastic integral equations with solutions being fuzzy stochastic processes.
In this case the notion of the stochastic Itô’s integral in the equation is crisp; that is, it has single-valued level sets.
The second aim of this paper is to show that there is no extension to more general diffusion terms.
American Psychological Association (APA)
Michta, Mariusz. 2016. Fuzzy Stochastic Differential Equations Driven by Semimartingales-Different Approaches. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1074725
Modern Language Association (MLA)
Michta, Mariusz. Fuzzy Stochastic Differential Equations Driven by Semimartingales-Different Approaches. Mathematical Problems in Engineering No. 2015 (2015), pp.1-9.
https://search.emarefa.net/detail/BIM-1074725
American Medical Association (AMA)
Michta, Mariusz. Fuzzy Stochastic Differential Equations Driven by Semimartingales-Different Approaches. Mathematical Problems in Engineering. 2016. Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1074725
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074725