Some distance bounds of branching processes and their diffusion limits
arXiv:1005.3758 · doi:10.3390/e22080874
Abstract
We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration is arbitrarily Poisson-distributed (leading to arbitrary type of criticality). Implications for asymptotic distinguishability behaviour in terms of contiguity and entire separation of the involved GWI are given, too. Furthermore, we determine the corresponding limit quantities for the context in which the two GWI converge to Feller-type branching diffusion processes, as the time-lags between observations tend to zero. Some applications to (static random environment like) Bayesian decision making and Neyman-Pearson testing are presented as well.
45 pages
References in corpus (7)
- Rényi Divergence and Kullback-Leibler Divergence
- Inferring change points in the COVID-19 spreading reveals the effectiveness of interventions
- Stochastic epidemics in a homogeneous community
- Stochastic epidemics in a heterogeneous community (Part III of the book Stochastic Epidemic Models and Inference)
- Statistical inference for epidemic processes in a homogeneous community (Part IV of the book Stochastic Epidemic Models and Inference)
- On Bregman Distances and Divergences of Probability Measures
- Introduction to statistical inference for infectious diseases