拼合扩散过程最小解的构造及其不变测度、可逆性与遍历性

CONSTRUCTION AND PROPERTIES OF COUPLED DIFFUSION PROCESS

§1.引言 本文讨论由算子Ω=+(c_(ij)(x))生成的相空间为E=R^1×Z的马氏过程,其中且系数满足下列条件:

By using the probability method we construct a Markov process with state space E=R^1×Z andinfinitesimal generatorΩ=(Ω_j)+(c_(ij)(x))whereΩ_j=(d/dx)(α_j(x)(d/dx))+b_j(x)(d/dx),x∈R^1,j∈Z.Furthermore, the sufficient and necessary conditions for the conservation, reversibility and existenceof invariant measure are given. The ergodic limit is given also.