SPECTRAL ANALYSIS OF BILATERAL BIRTH-DEATH PROCESSES: SOME NEW EXPLICIT EXAMPLES

被引：1

作者：

de la Iglesia, Manuel D. ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Ciudad De Mexico 04510, Mexico

来源：

ADVANCES IN APPLIED PROBABILITY | 2022年 / 54卷 / 04期

关键词：

Bilateral birth-death processes; orthogonal polynomials; spectral analysis; NONLINEAR BIRTH; CONTINUOUS-TIME; RANDOM-WALKS;

D O I：

10.1017/apr.2021.64

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the spectral analysis of several examples of bilateral birth-death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some probabilistic properties of the processes, such as recurrence, the invariant distribution (if it exists), and the probability current.

引用

页码：1193 / 1221

页数：29

共 35 条

[1] BECKERMANN B., 1995, APPL MATH, V23, P319
[2] CHIHARA T. S, 1968, INTRO ORTHOGONAL POL
[3] RANDOMIZED RANDOM WALKS
CONOLLY, B
[J]. SIAM REVIEW, 1971, 13 (01) : 81 - &
[4] The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers
de la Iglesia, Manuel D.
Juarez, Claudia
[J]. JOURNAL OF APPROXIMATION THEORY, 2020, 258
[5] Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures
Dette, Holger
Reuther, Bettina
[J]. JOURNAL OF PROBABILITY AND STATISTICS, 2010, 2010
[6] On a bilateral birth-death process with alternating rates
Antonio Di Crescenzo
Antonella Iuliano
Barbara Martinucci
[J]. Ricerche di Matematica, 2012, 61 (1) : 157 - 169
[7] Asymptotic Results for Random Walks in Continuous Time with Alternating Rates
Di Crescenzo, Antonio
Macci, Claudio
Martinucci, Barbara
[J]. JOURNAL OF STATISTICAL PHYSICS, 2014, 154 (05) : 1352 - 1364
[8] On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities
Di Crescenzo, Antonio
Martinucci, Barbara
[J]. SYMMETRY-BASEL, 2009, 1 (02): : 201 - 214
[9] DOMINGUEZ DE LA IGLESIA M, 2021, ORTHOGONAL POLYNOMIA
[10] Dunford N., 1988, LINEAR OPERATORS 2

← 1 2 3 4 →