Long-Range Dependence of Markov Chains in Discrete Time on Countable State Space
نویسندگان
چکیده
منابع مشابه
Ergodic Theory for Countable State Space Markov Chains
Here we want to see to what extent the results from Doeblin’s theory for finite state spaces extend to the case when the state space is countably infinite. Throughout we will use π to denote the row vector whose jth component is πj = ( E[ρj |X0 = j] )−1. Theorem (A). If j is transient, then πj = 0 = limn→∞(P)ij for all i. Proof. Because P(ρj = ∞|X0 = j) > 0, it is clear that πj = 0. Thus, all t...
متن کاملUniform CLT for Markov chains with a countable state space
Let (S,G, P ) be a probability space and let F be a set of measurable functions on S with an envelope function F finite everywhere. Let X1, X2, ... be a strictly stationary sequence of random variables with distribution P , and define the empirical measures Pn, based on {Xi}, as Pn = n−1 ∑n i=1 δXi . We say the uniform CLT holds over F , if n 1 2 (Pn − P ) converges in law, in the space l∞(F ) ...
متن کاملOn Continuous Time Markov Games with Countable State Space
This paper is a continuation of our papers [61 and [71 and is concerned with a continuous time Markov game in which the state space is countable and the action spaces of player I and player n are compact metric spaces. In the game, the players continuously observe the state of the system and then choose actions. As a result, the reward is paid to player I from player n and the system moves to a...
متن کاملThe CLT for Markov chains with a countable state space embedded in the space lp
We nd necessary and su cient conditions for the CLT for Markov chains with a countable state space embedded in the space lp for p¿1. This result is an extension of the uniform CLT over the family of indicator functions in Levental (Stochastic Processes Appl. 34 (1990) 245–253), where the result is equivalent to our case p=1. A similar extension for the uniform CLT over a family of possibly unbo...
متن کاملFormalization of Finite-State Discrete-Time Markov Chains in HOL
The mathematical concept of Markov chains is widely used to model and analyze many engineering and scientific problems. Markovian models are usually analyzed using computer simulation, and more recently using probabilistic model-checking but these methods either do not guarantee accurate analysis or are not scalable. As an alternative, we propose to use higher-order-logic theorem proving to rea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2007
ISSN: 0021-9002,1475-6072
DOI: 10.1017/s0021900200003727