Branching diffusion processes in periodic media
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 214-236
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We consider branching diffusion processes in $\mathbf R^d$ in periodic media. The movement of particles in $\mathbf R^d$ is described by a stochastic differential equation with periodic coefficients. We study the asymptotic behavior of the mean number of particles in an arbitrary bounded set as $t\to\infty$. In the case when an initial configuration cosists of one particle at a point $x\in\mathbf R^d$ we obtain the answer for $d\leqslant 3$. In the case when an initial configuration is random and has a density with a compact support the answer is obtained for any $d$.
@article{ZNSL_2024_535_a14,
author = {M. V. Platonova and K. S. Ryadovkin},
title = {Branching diffusion processes in periodic media},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {214--236},
publisher = {mathdoc},
volume = {535},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a14/}
}
M. V. Platonova; K. S. Ryadovkin. Branching diffusion processes in periodic media. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 214-236. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a14/