Branching diffusion processes in periodic media

M. V. Platonova   ; K. S. Ryadovkin

Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 214-236

Résumé

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 $d$.

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