Abstract
In this paper we study the convergence of dynamical discrete web (DyDW) to the dynamical Brownian web (DyBW) in a path space topology. We show that almost surely the DyBW has RCLL paths taking values in an appropriate metric space, and as a sequence of RCLL paths, the rescaled DyDW converges to the DyBW. This proves weak convergence of the DyDW process to the DyBW process.
Dans cet article, nous étudions la convergence du Dynamical Discrete Web (DyDW) vers le Dynamical Brownian Web (DyBW) pour la topologie associée à l’espace des trajectoires. Nous démontrons que presque sûrement le DyBW possède des trajectoires càdlàg à valeurs dans un espace métrique approprié et, en tant que suite de trajectoires càdlàg, le DyDW re-échelonné converge vers le DyBW. Ceci établit la convergence faible du processus DyDW vers le DyBW.
Acknowledgements
Part of the work on this paper was done when K.S. visited K.R at NYU Abu Dhabi. Both the authors wish to thank NYU Abu Dhabi for hospitality and support. Both the authors thank the referee for his/her comments which led to a significant improvement of this paper.
Citation
Krishnamurthi Ravishankar. Kumarjit Saha. "Convergence of the dynamical discrete web to the dynamical Brownian web." Ann. Inst. H. Poincaré Probab. Statist. 60 (3) 1788 - 1813, August 2024. https://doi.org/10.1214/23-AIHP1376
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