Abstract:In this report, I will introduce the semi-group formulation of the SPDE. And I shall give a stability analysis for filtering algorithm based on spectral methods from two aspects.1. Asymptotic analysis of the relationship between the number of spectra and errors in spectral methods.2. Analysis of the stability of spectral algorithm by time discretization
AbstractWe examine the asymptotic behaviors of solutions to Hamilton-Jacobi equations with state constraints while varying the underlying domains. We establish a connection between the convergence of these solutions and the regularity of the additive eigenvalues in relation to the domains. To accomplish this, we introduce a framework based on Mather measures that enables us to compute the one-s...