Characterization of Stochastic Mean‐Field Type
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| Authors: | Limin Ma Yan Li Tianliang Zhang |
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| Affiliation: | 1. College of Science and Information, Qingdao Agricultural University, China;2. Electrical Engineering and Automation, Shandong University of Science and Technology, China;3. School of Automation Science and Engineering, South China University of Technology, China |
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| Abstract: |  index of mean‐field stochastic differential equations (SDE) is investigated in this paper. For systems with state‐ and input‐dependent noise, we obtain a sufficient condition of  index larger than some λ>0 via the solvability of differential Riccati equations (DRE). Especially, a necessary and sufficient condition is given for mean‐field SDE with state‐dependent noise, which generalize the corresponding results of classical stochastic systems to the mean‐field stochastic models. |
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| Keywords: | Mean field
index coupled matrix‐valued equations continuous‐time stochastic systems |
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index of mean‐field stochastic differential equations (SDE) is investigated in this paper. For systems with state‐ and input‐dependent noise, we obtain a sufficient condition of 
index larger than some λ>0 via the solvability of differential Riccati equations (DRE). Especially, a necessary and sufficient condition is given for mean‐field SDE with state‐dependent noise, which generalize the corresponding results of classical stochastic systems to the mean‐field stochastic models.