Orthogonal Polynomials on R+ and Birth-death Processes with Killing
نویسندگان
چکیده
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.
منابع مشابه
Weighted Sums of Orthogonal Polynomials Related to Birth-Death Processes with Killing
We consider sequences of orthogonal polynomials arising in the analysis of birth-death processes with killing. Motivated by problems in this stochastic setting we discuss criteria for convergence of certain weighted sums of the polynomials. AMS Subject Classifications: 42C05, 60J80.
متن کاملBirth-death Processes with Killing: Orthogonal Polynomials and Quasi-stationary Distributions
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 کاملOn the 2-orthogonal polynomials and the generalized birth and death processes
The birth and death processes are closely related to the orthogonal polynomials. The latter allows determining the stochastic matrix associated with these processes. Let us also note that these processes are stationary Markov processes whose state space is the nonnegative integers. Many authors treated the question of the existing relationship between the birth and death processes and the ortho...
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 کاملMultivariate Krawtchouk Polynomials and Composition Birth and Death Processes
This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of functions defined on each of N multinomial trials. The dual multivariate Krawtchouk polynomials, which also have a polynomial structure, are seen to occur natural...
متن کامل