Extinction Probability in A Birth-Death Process with Killing
نویسندگان
چکیده
منابع مشابه
Extinction times for a birth-death process with weak competition
We consider a birth-death process with the birth rates iλ and death rates iμ+i(i−1)θ, where i is the current state of the process. A positive competition rate θ is assumed to be small. In the supercritical case when λ > μ this process can be viewed as a demographic model for a population with a high carrying capacity around λ−μ θ . The article reports in a self-contained manner on the asymptoti...
متن کاملExtinction times for a birth-death process with two phases.
Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural mo...
متن کاملBirth-death Processes with Killing
The purpose of this note is to point out that Karlin and McGregor’s integral representation for the transition probabilities of a birth-death process on a semi-infinite lattice with an absorbing bottom state remains valid if one allows the possibility of absorption into the bottom state from any other state. Conditions for uniqueness of the minimal transition function are also given.
متن کاملQuasi-stationary Distributions for Birth-death Processes with Killing
The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state (killing) is possible from any state rather than just one state. The purpose of this paper is to in...
متن کاملOrthogonal Polynomials on R+ and Birth-death Processes with Killing
The purpose of this paper is to extend some results of Karlin and McGregor’s and Chihara’s concerning the three-terms recurrence relation for polynomials orthogonal with respect to a measure on the nonnegative real axis. Our findings are relevant for the analysis of a type of Markov chains known as birth-death processes with killing.
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2005
ISSN: 0021-9002,1475-6072
DOI: 10.1239/jap/1110381380