Fuzzy stochastic differential equations driven by fractional Brownian motion

In this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an appr...

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Bibliographic Details
Published in:Advances in difference equations 2021-01, Vol.2021 (1), p.1-17, Article 16
Main Authors: Jafari, Hossein, Malinowski, Marek T., Ebadi, M. J.
Format: Article
Language:English
Subjects:
Analysis
Approximation
Brownian motion
Difference and Functional Equations
Differential equations
Fractional Brownian motion
Functional Analysis
Fuzzy set theory
Fuzzy stochastic differential equation
Fuzzy stochastic processes
Hybrid systems
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Randomness
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Summary:In this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions. As an example, in financial models, we obtain the solution for an equation with linear coefficients.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-03181-z