Abstract
This paper considers the properties of the waiting time to survive forever of the supercritical age-dependent branching process modified with an immigration component. Conditioning on ultimate extinction of the process we analyze the conditional distribution of the cycle length and its expectation. We then derive and give estimates of the conditional expected total progeny of a cycle and its higher moments. In general, the model originates from the problem of estimating the waiting time to a successful experiment in industrial wastewater treatment by bacterial culture systems. Computer runs were made for two reproduction laws and different reproduction means.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
