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Speed of extinction for continuous-state branching processes in a weakly subcritical Lévy environment
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Natalia Cardona-Tobón, Juan Carlos Pardo
Journal:

Journal of Applied Probability , First View

Published online by Cambridge University Press:

01 December 2023, pp. 1-23
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We continue with the systematic study of the speed of extinction of continuous-state branching processes in Lévy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime under the assumption that the branching mechanism is regularly varying. We extend recent results of Li and Xu (2018) and Palau et al. (2016), where it is assumed that the branching mechanism is stable, and complement the recent articles of Bansaye et al. (2021) and Cardona-Tobón and Pardo (2021), where the critical and the strongly and intermediate subcritical cases were treated, respectively. Our methodology combines a path analysis of the branching process together with its Lévy environment, fluctuation theory for Lévy processes, and the asymptotic behaviour of exponential functionals of Lévy processes. Our approach is inspired by the last two previously cited papers, and by Afanasyev et al. (2012), where the analogue was obtained.

Contents
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp vii-xi
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9 - Envelopes of positive self-similar Markov processes
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 227-251
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6 - Spatial fluctuations in one dimension
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 153-182
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14 - Spatial fluctuations and the unit sphere
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 351-382
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Dedication
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp v-vi
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2 - Lévy processes
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 27-57
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Index
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 458-463
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Acknowledgements
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp xx-xx
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16 - Windings and up-crossings of stable processes
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 412-428
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3 - Stable processes
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 58-77
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Notation
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp xii-xviii
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7 - Doney–Kuznetsov factorisation and the maximum
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 183-205
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13 - Radial reflection and the deep factorisation
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 330-350
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15 - Applications of radial excursion theory
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 383-411
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4 - Hypergeometric Lévy processes
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 78-114
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1 - Stable distributions
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 1-26
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10 - Asymptotic behaviour for path transformations
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 252-285
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Appendix
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 429-445
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5 - Positive self-similar Markov processes
Andreas E. Kyprianou, University of Bath, Juan Carlos Pardo
Book:

Stable Lévy Processes via Lamperti-Type Representations

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16 March 2022

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07 April 2022, pp 115-152
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Speed of extinction for continuous-state branching processes in a weakly subcritical Lévy environment

Contents

9 - Envelopes of positive self-similar Markov processes

6 - Spatial fluctuations in one dimension

14 - Spatial fluctuations and the unit sphere

Dedication

2 - Lévy processes

Index

Acknowledgements

16 - Windings and up-crossings of stable processes

3 - Stable processes

Notation

7 - Doney–Kuznetsov factorisation and the maximum

13 - Radial reflection and the deep factorisation

15 - Applications of radial excursion theory

4 - Hypergeometric Lévy processes

1 - Stable distributions

10 - Asymptotic behaviour for path transformations

Appendix

5 - Positive self-similar Markov processes

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34 results