Weak convergence of sequences of semimartingales with applications to multitype branching processes
- 1 March 1986
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 18 (01) , 20-65
- https://doi.org/10.1017/s0001867800015585
Abstract
The paper is devoted to a systematic discussion of recently developed techniques for the study of weak convergence of sequences of stochastic processes. The methods described make essential use of the semimartingale structure of the processes. Sufficient conditions for tightness including the results of Rebolledo are derived. The techniques are applied to a special class of processes, namely the D-semimartingales. Applications to multitype branching processes are given.Keywords
This publication has 11 references indexed in Scilit:
- On tightness and stopping timesStochastic Processes and their Applications, 1983
- Diffusion approximation of the two-type Galton-Watson process with mean matrix close to the identityJournal of Multivariate Analysis, 1982
- Some Useful Functions for Functional Limit TheoremsMathematics of Operations Research, 1980
- Stopping Times and TightnessThe Annals of Probability, 1978
- Limiting diffusions for population-size dependent branching processesJournal of Applied Probability, 1977
- Semigroups of Conditioned Shifts and Approximation of Markov ProcessesThe Annals of Probability, 1975
- Conditional Distributions and TightnessThe Annals of Probability, 1974
- Diffusion Approximations of Branching ProcessesThe Annals of Mathematical Statistics, 1971
- The Limit of a Sequence of Branching ProcessesProbability Theory and Related Fields, 1967
- Limit Theorems for Stochastic ProcessesTheory of Probability and Its Applications, 1956