Stochastic Processes ( Fall 2017 ) Lecture : 10 Invariant Distributions
نویسندگان
چکیده
Suppose C is a closed recurrent communicating class for a Markov chain, if we restrict the chain on this class, the result is still a Markov chain with state space C. The resulting Markov chain is irreducible and recurrent. In this lecture, we will focus on the long-time behavior of irreducible and recurrent Markov chain. First, we have the following related definition. Definition 10.1. For a Markov chain, a measure ~λ is any row vector (λi, i ∈ I) with non-negative entries. We say that ~λ is invariant if ~λP = ~λ In short, what we will discuss is the invariant measure for probability and expectation.
منابع مشابه
Math 564 : Applied Stochastic Processes ( Fall 2017 ) Lecture : 10 Invariant Distributions
Suppose C is a closed recurrent communicating class for a Markov chain, if we restrict the chain on this class, the result is still a Markov chain with state space C. The resulting Markov chain is irreducible and recurrent. In this lecture, we will focus on the long-time behavior of irreducible and recurrent Markov chain. First, we have the following related definition. Definition 10.1. For a M...
متن کاملLecture notes for Modelling in Biology II: Stochastic processes and networks
2 Some Useful Mathematics 5 2.1 Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 The meaning of probability . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Basic definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3 Expectations of outcomes from probability distributions . . . . . . . . . . 8 2.1.4 Continuo...
متن کاملSpring 2008 STA 293 : Stochastic Processes & Bayesian
Markov chains are among the simplest stochastic processes, just one step beyond iid sequences of random variables. Traditionally they’ve been used in modelling a variety of physical phenomena, but recently interest has grown enormously due to their applicability in facilitating Bayesian computation. These lecture notes and lectures are intended to introduce the elements of markov chain theory, ...
متن کامل"Harmonic Analysis: Smooth and Non-smooth."1em Introduction to the Conference: Historical context, Reading list, Basic definitions, some relevant results, and an Outline of the Ten Lectures by Jorgensen. 1em CBMS conference to be held at Iowa State University, June 4–8, 2018
Lecture 1. Harmonic Analysis of Measures: Analysis on Fractals Lecture 2. Spectra of measures, tilings, and wandering vectors Lecture 3. The universal tiling conjecture in dimension one and operator fractals Lecture 4. Representations of Cuntz algebras associated to quasi-stationary Markov measures Lecture 5. The Cuntz relations and kernel decompositions Lecture 6. Harmonic analysis of wavelet ...
متن کامل