Approximation of Arbitrary Dirichlet Processes by Markov Chains 1);2)
نویسنده
چکیده
We prove that any Hunt process on a Hausdorr topological space associated with a Dirichlet form can be approximated by a Markov chain in a canonical way. This also gives a new and \more explicit" proof for the existence of Hunt processes associated with strictly quasi-regular Dirichlet forms on general state spaces.
منابع مشابه
Dirichlet forms: Some infinite dimensional examples
The theory of Dirichlet forms deserves to be better known. It is an area of Markov process theory that uses the energy of functionals to study a Markov process from a quantitative point of view. For instance, the recent notes of Saloff-Coste [S-C] use Dirichlet forms to analyze Markov chains with finite state space, by making energy comparisons. In this way, information about a simple chain is ...
متن کاملEstimation of the Entropy Rate of ErgodicMarkov Chains
In this paper an approximation for entropy rate of an ergodic Markov chain via sample path simulation is calculated. Although there is an explicit form of the entropy rate here, the exact computational method is laborious to apply. It is demonstrated that the estimated entropy rate of Markov chain via sample path not only converges to the correct entropy rate but also does it exponential...
متن کاملLinear functionals and Markov chains associated with Dirichlet processes
By investigating a Markov chain whose limiting distribution corresponds to that of the Dirichlet process we are able directly to ascertain conditions for the existence of linear functionals of that process. Together with earlier analyses we are able to characterize those functionals which are a.s. finite in terms of the parameter measure of the process. We also show that the appropriate Markov ...
متن کاملBcp 2 : an Environment to Run Markov Chains for Bayesian Change Point Problems
1 Abstract We study a Bayesian nonparametric model for change point problems and propose a Markov chain method to approximate the posterior distributions of interest. The program developed to run the Gibbs sampler is called BCP 2 (Bayesian Change Point Problem). Its user-friendly graphical interface enables the user to enter the values of some parameters of interest and immediately obtain the c...
متن کاملDirichlet Forms on Laakso and Some Barlow-Evans Fractals of Arbitrary Dimension
In this paper we explore two constructions of the same family of metric measure spaces. The first construction was introduced by Laakso in 2000 where he used it as an example that Poincaré inequalities can hold on spaces of arbitrary Hausdorff dimension. This was proved using minimal generalized upper gradients. Following Cheeger’s work these upper gradients can be used to define a Sobolev spac...
متن کامل