EXERCISE 3.1. Let be an irreducible transition matrix on X, and let be a probability distribution on X. Show that the transition matrix P(x,y) V(x,y) x(y) (y.x) x(x)V(x,y) 1- ^ if y + x, if y = z (=)V(=,x) Σ Ψ(1,2) x(x)V (1,2) 2:27x defines a reversible Markov chain with stationary distribution. ^

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 13CM
icon
Related questions
Question

V7

EXERCISE 3.1. Let V be an irreducible transition matrix on X, and let a be a
probability distribution on X. Show that the transition matrix
V(1, y)
T(y)V (y.1)
T(2)V(1,y)
if y + x,
P(r, y) =
1- E ♥(r, z)
if y = r
(z*z)4(r)
defines a reversible Markov chain with stationary distribution n.
Transcribed Image Text:EXERCISE 3.1. Let V be an irreducible transition matrix on X, and let a be a probability distribution on X. Show that the transition matrix V(1, y) T(y)V (y.1) T(2)V(1,y) if y + x, P(r, y) = 1- E ♥(r, z) if y = r (z*z)4(r) defines a reversible Markov chain with stationary distribution n.
Expert Solution
steps

Step by step

Solved in 3 steps with 12 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage