THE EXISTENCE OF HAMILTONIAN DYNAMIC PROCESSES

In this paper, by using Hille-Yosida theorem, we construot dynamio prooesses whose Hamiltonian is given by H(x)=\sum_\mid x-v 1^2=1\left|x_u-x_0\right|^2+\sum_u \in s \Phi\left(x_u\right); where H（x） is defined on a non-compaet （R^d）^s. We prove that the limit of Hamiltonian finite dimensions Gibbs state is a reversible measure of the construoted Markov processes.