Stochastic coalescence with homogeneous-like interaction rates

Nicolas Fournier (1) , Eva Loecherbach (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We study infinite systems of particles characterized by their masses. Each pair of particles with masses x and y coalesces at a given rate $K(x, y)$. We consider, for each $\lambda\in\mathbb{R}$, a class of homogeneous (or homogeneous-like) coagulation kernels $K$. We show that such processes exist as strong Markov Feller processes with values in $\ell_\lambda$ , the set of ordered $[0,\infty]$-valued sequences $(m_i )_{i\geq 1}$ such that $\sum_{i\geq 1} m_i^\lambda < \infty$.

Mots clés: Coalescence; Homogeneous coagulation kernels; Stochastic interacting particle systems

Domaines: Probabilités [math.PR]

Nicolas Fournier, Eva Loecherbach. Stochastic coalescence with homogeneous-like interaction rates. Stochastic Processes and their Applications, 2009, 119 (1), pp.167-189. ⟨10.1016/j.spa.2008.01.007⟩. ⟨hal-00731540⟩