Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses
Open Access
- 1 October 1998
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 26 (4) , 1407-1432
- https://doi.org/10.1214/aop/1022855868
Abstract
We use the exploration process introduced in a previous work to develop a new construction of superprocesses with a general branching mechanism. This construction depends on a path-valued process called the Lévy snake, which is of independent interest. Our method of proof involves a calculation of the Laplace functional of the occupation field of the Lévy snake. This calculation relies on an evaluation of the corresponding moment functionals, which requires precise information about the underlying genealogical structure.Keywords
This publication has 10 references indexed in Scilit:
- Branching processes in Lévy processes: the exploration processThe Annals of Probability, 1998
- The Brownian snake and solutions of Δu=u 2 in a domainProbability Theory and Related Fields, 1995
- An Introduction to Branching Measure-Valued ProcessesPublished by American Mathematical Society (AMS) ,1994
- The uniform random tree in a Brownian excursionProbability Theory and Related Fields, 1993
- Superprocesses and Partial Differential EquationsThe Annals of Probability, 1993
- A class of path-valued Markov processes and its applications to superprocessesProbability Theory and Related Fields, 1993
- Branching Particle Systems and SuperprocessesThe Annals of Probability, 1991
- Historical processesMemoirs of the American Mathematical Society, 1991
- Equilibrium Distributions of Branching ProcessesPublished by Walter de Gruyter GmbH ,1988
- Fluctuation theory in continuous timeAdvances in Applied Probability, 1975