Almost Sure Stabilizability of Controlled Degenerate Diffusions

@article{Bardi2005AlmostSS,
  title={Almost Sure Stabilizability of Controlled Degenerate Diffusions},
  author={Martino Bardi and Annalisa Cesaroni},
  journal={SIAM J. Control and Optimization},
  year={2005},
  volume={44},
  pages={75-98}
}
We develop a direct Lyapunov method for the almost sure open-loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes. The infinitesimal decrease condition for a Lyapunov function is a new form of Hamilton-Jacobi-Bellman partial differential inequality of 2nd order. We give local and global versions of the First and Second Lyapunov Theorems assuming the existence of a lower semicontinuous Lyapunov function satisfying such inequality in the viscosity sense… CONTINUE READING

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