Exponential Ergodicity Rate Of Diffusion Processes With Markov Switching And Inverse Iteration Of P-Laplacian On Trees

This dissertation mainly studies the stability of the switching diffusion processes with markov transition and the estimation of the prnncipal eigenvalues of the p-Laplacian on trees.For the diffusion processes with Markov switching?X_t,?_t?t?0 on R₊ × S,we study the ex-ponential stability of the processes,including the criteria conditions for exponential ergodicity of diffusion processes with switching and the explicit estimation of exponential ergodicity rate.First of all,using Lyapunov function theory,infinitesimal generating element and M-matrix theory,we give respectively two kinds of criteria of?X_t,?_t?t?0 for exponential ergodicity.Sec-ondly,under the fixed environment At = i,i ? S,R₊× i upper origin reflection boundary one-dimensional that diffusion process?X_t,i?is a random order preserving and time-invariant one-dimensional diffusion process?X_t,i?,we are discussed the exponential ergodicity rates of?X_t,??_t?t?0 by coupling method and martingales theory.For the p-Laplacian eigenvalue estimation problem on trees,this dissertation studies the root for the Dirichlet boundary p-Laplacian eigenvalue numerical approximation,we put for-ward the p-Laplacian principal eigenvalue inverse iteration method and approximation program and give approximation that the given approximation program can be monotone convergence in main eigenvalue ?_p,q.Finally,we give the main eigenvalue inverse iteration method and approximate convergence theory of the p-Laplacian on trees.