A limit order book is a financial trading mechanism that keeps track of orders made by traders, and allows to execute them in the future. In this talk I will present a simple model of a one-sided limit order book, which is modeled as a point process evolving over time.I will discuss two aspects of this model: the asymptotic behavior of the so-called price process (the extremal point) and the scaling limit of the entire measure-valued process. The proofs rely on a coupling with a branching random walk with a barrier, and on a characterization of regenerative real trees due to Weill [Ann. Probab. 2007].
- Séminaire informel de Probabilités et Statistiques