Ergodicities and exponential ergodicities of Dawson--Watanabe type processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 342-368
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Under natural assumptions, we prove the ergodicities and exponential
ergodicities in Wasserstein and total variation distances of Dawson–Watanabe
superprocesses without or with immigration. The strong Feller property in the
total variation distance is derived as a by-product. The key of the approach
is a set of estimates for the variations of the transition probabilities.
The estimates in Wasserstein distance are derived from an upper bound of the
kernels induced by the first moment of the superprocess. Those in total
variation distance are based on a comparison of the cumulant semigroup of the
superprocess with that of a continuous-state branching process. The results
improve and extend considerably those of Friesen [Long-Time Behavior
for Subcritical Measure-Valued Branching Processes with Immigration,
arXiv:1903.05546, 2019] and Stannat [J. Funct. Anal., 201 (2003),
pp. 185–227; Ann. Probab., 31 (2003), pp. 1377–1412]. We also
show a connection between the ergodicities of the immigration superprocesses
and decomposable distributions.
Keywords:
Dawson–Watanabe superprocess, coupling, strong Feller property, stationary distribution, exponential ergodicity.
Mots-clés : immigration
Mots-clés : immigration
@article{TVP_2021_66_2_a6,
author = {Z. Li},
title = {Ergodicities and exponential ergodicities of {Dawson--Watanabe} type processes},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {342--368},
publisher = {mathdoc},
volume = {66},
number = {2},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a6/}
}
Z. Li. Ergodicities and exponential ergodicities of Dawson--Watanabe type processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 342-368. http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a6/