# A level-1 Limit Order book with time dependent arrival rates

## TL;DR

This paper introduces a stochastic model for level-1 limit order book dynamics with time-dependent arrival rates, demonstrating that the price process converges to a Brownian meander in the diffusion limit.

## Contribution

It extends existing models by incorporating time-dependent order arrival rates and characterizes the price process as a Brownian meander in the diffusion limit.

## Key findings

- Price dynamics are endogenous and driven by market transactions.
- The diffusion limit of the price process is a Brownian meander.
- The model generalizes previous work by including time-dependent rates.

## Abstract

We propose a simple stochastic model for the dynamics of a limit order book, extending the recent work of Cont and de Larrard (2013), where the price dynamics are endogenous, resulting from market transactions. We also show that the conditional diffusion limit of the price process is the so-called Brownian meander.