Skip to main content Accessibility help
×
Home
Hostname: page-component-6c8bd87754-clkrv Total loading time: 0.238 Render date: 2022-01-18T15:13:40.249Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

3 - Consistency of Finite Multivariate Markov Chains

from Part One - Consistencies

Published online by Cambridge University Press:  18 September 2020

Tomasz R. Bielecki
Affiliation:
Illinois Institute of Technology
Jacek Jakubowski
Affiliation:
Uniwersytet Warszawski, Poland
Mariusz Niewȩgłowski
Affiliation:
Politechnika Warszawska, Poland
Get access

Summary

In this chapter the concept of strong Markov consistency and the concept of weak Markov consistency for finite time-inhomogeneous multivariate Markov chains is introduced and studied. In particular, necessary and sufficient conditions for both types of Markov consistency are given. The main tool used here is the semimartingale characterization of finite Markov chains. In addition, operator interpretation of a sufficient condition for strong Markov consistency and a necessary condition for weak Markov consistency are provided. By definition, strong Markov consistency implies the weak Markov consistency. In this chapter we provide sufficient condition for the reverse implication to hold.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Send book to Kindle

To send this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Send book to Dropbox

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox.

Available formats
×

Send book to Google Drive

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

Available formats
×