Necessary and sufficient conditions for near-optimal harvesting control problem of stochastic age-dependent system

2013 ◽  
Vol 221 ◽  
pp. 394-402 ◽  
Author(s):  
Qimin Zhang ◽  
Dongmei Wei
Keyword(s):  
Control Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Optimal Harvesting ◽  
Age Dependent ◽  
Necessary And Sufficient

A branching process with disasters

1975 ◽  
Vol 12 (1) ◽  
pp. 47-59 ◽  
Author(s):  
Norman Kaplan ◽  
Aidan Sudbury ◽  
Trygve S. Nilsen
Keyword(s):  
Asymptotic Behavior ◽  
Renewal Process ◽  
Branching Process ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Population Process ◽  
Age Dependent ◽  
The Mean ◽  
Necessary And Sufficient

A population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process. Each particle alive at the time of a disaster, survives it with probability p and the survival of any particle is assumed independent of the survival of any other particle. The asymptotic behavior of the mean of the process is determined and as a consequence, necessary and sufficient conditions are given for extinction.

A branching process with disasters

1975 ◽  
Vol 12 (01) ◽  
pp. 47-59 ◽  
Author(s):  
Norman Kaplan ◽  
Aidan Sudbury ◽  
Trygve S. Nilsen
Keyword(s):  
Asymptotic Behavior ◽  
Renewal Process ◽  
Branching Process ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Population Process ◽  
Age Dependent ◽  
The Mean ◽  
Necessary And Sufficient

A population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process. Each particle alive at the time of a disaster, survives it with probability p and the survival of any particle is assumed independent of the survival of any other particle. The asymptotic behavior of the mean of the process is determined and as a consequence, necessary and sufficient conditions are given for extinction.

Terminal Control with Guaranteed Accuracy Based on the Interval System Model

Vestnik MEI ◽  
2021 ◽  
pp. 115-121
Author(s):  
Nikita V. Skribitsky ◽  
Keyword(s):  
Control Problem ◽  
A Priori ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Problem Solution ◽  
Terminal Control ◽  
Interval System ◽  
Interval Model ◽  
Necessary And Sufficient ◽  
Solution Accuracy

The problem of optimal terminal control of a linear stationary system the parameters of which are known with accuracy up to intervals is formulated, and the necessary and sufficient conditions for its stability and controllability are determined. A set of control actions that guarantee the specified accuracy of solving the optimal control problem given an interval model of the initial data is obtained. The necessary and sufficient conditions for the existence of this set are determined, and algorithms for its construction and obtaining its rectangular subset of the maximum volume are developed. A priori requirements for the accuracy of identifying the system parameters are formulated taking into account the requirements for the control problem solution accuracy.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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