Existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non-Lipschitzian condition |
| |
| Institution: | 1. Institute of Contemporary Mathematics, Henan University, Kaifeng, Henan 475001, China;2. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA;3. Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210023, China;4. Department of Mathematics, College of Science, Swansea University, Swansea, SA2 8PP, UK;1. Department of Electrical Engineering, National Tsing Hua University, Hsinchu, 30013, Taiwan;2. Department of Electrical Engineering, Yuan Ze University, Chung-Li, 32003, Taiwan;3. The College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266510, China;1. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland;2. Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland;3. Institute of Computer Science, Polish Academy of Sciences, Jana Kazimierza 5, 01-248 Warsaw, Poland |
| |
| Abstract: | This paper makes a research into a class of fuzzy stochastic differential equations (FSDEs) driven by a continuous local martingale under the non-Lipschitzian condition. Such equations can be useful in modelling of hybrid systems, where the phenomena are subjected to two kinds of uncertainties: randomness and fuzziness, simultaneously. The solutions of FSDEs are the fuzzy stochastic processes, and their uniqueness is considered to be in a strong sense. Thus, the existence and uniqueness of solutions to FSDEs under the non-Lipschitzian condition is first proven. And the continuity of solutions to FSDEs with respect to the initial data or the coefficients of the equations is investigated. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
