@article{BURACZEWSKI2023199,
title = {Solutions of kinetic-type equations with perturbed collisions},
journal = {Stochastic Processes and their Applications},
volume = {159},
pages = {199-224},
year = {2023},
issn = {0304-4149},
doi = {https://doi.org/10.1016/j.spa.2023.01.014},
url = {https://www.sciencedirect.com/science/article/pii/S0304414923000236},
author = {Dariusz Buraczewski and Piotr Dyszewski and Alexander Marynych},
keywords = {Additive martingale, Branching random walk, Inhomogeneous smoothing transform, Kac model, Kinetic equation, Random trees},
abstract = {We study a class of kinetic-type differential equations ∂ϕt/∂t+ϕt=Q̂ϕt, where Q̂ is an inhomogeneous smoothing transform and, for every t≥0, ϕt is the Fourier–Stieltjes transform of a probability measure. We show that under mild assumptions on Q̂ the above differential equation possesses a unique solution and represent this solution as the characteristic function of a certain stochastic process associated with the continuous time branching random walk pertaining to Q̂. Establishing limit theorems for this process allows us to describe asymptotic properties of the solution, as t→∞.}
}