Skip to main content Accessibility help
×
Home
Hostname: page-component-8bbf57454-s7zjg Total loading time: 0.214 Render date: 2022-01-26T04:37:32.394Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Solutions of ordinary differential equations as limits of pure jump markov processes

Published online by Cambridge University Press:  14 July 2016

Thomas G. Kurtz*
Affiliation:
University of Wisconsin

Extract

In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 

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.)

References

[1] Dynkin, E. B. (1965) Markov Processes I. Academic Press, New York, and Springer-Verlag, Berlin-Göttingen-Heidelberg.CrossRefGoogle Scholar
[2] Kemeny, J. G. and Snell, J. L. (1962) Mathematical Models in the Social Sciences. Ginn and Company, Boston.Google Scholar
[3] Kurtz, T. G. (1969) Extensions of Trotter's operator semigroup approximation theorems. J. Functional Anal. 3, 111132.CrossRefGoogle Scholar
63
Cited by

Send article to Kindle

To send this article 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. 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.

Solutions of ordinary differential equations as limits of pure jump markov processes
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and 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 <service> account. Find out more about sending content to Dropbox.

Solutions of ordinary differential equations as limits of pure jump markov processes
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and 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 <service> account. Find out more about sending content to Google Drive.

Solutions of ordinary differential equations as limits of pure jump markov processes
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *