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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 3830529, 13 pages
Research Article

Bipartite Fuzzy Stochastic Differential Equations with Global Lipschitz Condition

Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland

Received 27 April 2016; Revised 25 September 2016; Accepted 13 October 2016

Academic Editor: Leonid Shaikhet

Copyright © 2016 Marek T. Malinowski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce and analyze a new type of fuzzy stochastic differential equations. We consider equations with drift and diffusion terms occurring at both sides of equations. Therefore we call them the bipartite fuzzy stochastic differential equations. Under the Lipschitz and boundedness conditions imposed on drifts and diffusions coefficients we prove existence of a unique solution. Then, insensitivity of the solution under small changes of data of equation is examined. Finally, we mention that all results can be repeated for solutions to bipartite set-valued stochastic differential equations.