This note addresses certain stability properties of the nonlinear filtering equation in discrete time. The available positive and negative results indicate that much depends on the structure of the signal state space, its ergodic properties and observations regularity. We show that certain predicting estimates are stable under surprisingly general assumptions.

Abstract. We study periodic homogenization problems for second-order pde in halfspace type domains with Neumann boundary conditions. In particular, we are interested in “singular problems” for which it is necessary to determine both the homogenized equation and boundary conditions. We provide new results for fully nonlinear equations and boundary conditions. Our results extend previous work of ...

We study the ergodic problem for fully nonlinear operators which may be singular or degenerate when at least one of components gradient vanishes. extend here results in [ 16 ], 10 24 ].

Abstract We extract quantitative information (specifically, a rate of metastability in the sense Terence Tao) from proof due to Kazuo Kobayasi and Isao Miyadera, which shows strong convergence for Cesàro means non-expansive maps on Banach spaces.