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Characterization of Stochastic Mean‐Field Type Index
Authors:Limin Ma  Yan Li  Tianliang Zhang
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
Abstract:urn:x-wiley:asjc:media:asjc1658:asjc1658-math-0004 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 urn:x-wiley:asjc:media:asjc1658:asjc1658-math-0005 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.
Keywords:Mean field      index  coupled matrix‐valued equations  continuous‐time stochastic systems
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