Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Let {X(t)} be a continuous-time Markov chain with stationary distribution. We sample the chain at times given by an independent Poisson process: let N(t)

image text in transcribed 


Let {X(t)} be a continuous-time Markov chain with stationary distribution. We sample the chain at times given by an independent Poisson process: let N(t) be a Poisson process with rate a, independent of the Markov chain, and define Y, = X(T +), the value taken by X immediately after the epoch T, of the nth arrival of N. Show that {Y} is a discrete-time Markov chain with the same stationary distribution as X.

Step by Step Solution

There are 3 Steps involved in it

Step: 1

Here are the steps to show that Y is a discretetime Markov chain with the same stationary distributi... blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers

Authors: Roy D. Yates, David J. Goodman

3rd edition

1118324560, 978-1118324561

More Books

Students also viewed these Finance questions

Question

Discuss the roles of metacognition in learning and remembering.

Answered: 1 week ago

Question

How do you think adults might react in a similar experiment?

Answered: 1 week ago