Abstract:

State space models(SSMs) provide a general framework for studying stochastic processes, which has been applied in revealing the true underlying economic processes of an economy, recognizing cellphone signals, detecting the loaction of an airplane on a radar screen, et al. In this paper, we study the Markov state space models by modeling the space transformation with reproducing kernel Hilbert space. Not only the existence and uniqueness of solutions are given, but also the error is estimate in L² spaces. We applied our method in Visibility prediction at airport in National Post-Graduate Mathematical Contest in Modeling supported by China Academic Degrees & Graduate Education Development Center.

Key words: State Space Model, Function Reconstruction, Kernel Method, Autoregression