## Journal of Applied Probability

- J. Appl. Probab.
- Volume 51, Number 3 (2014), 625-639.

### Coupling limit order books and branching random walks

#### Abstract

We consider a model for a one-sided limit order book proposed by Lakner, Reed and Stoikov (2013). We show that it can be coupled with a branching random walk and use this coupling to answer a nontrivial question about the long-term behavior of the price. The coupling relies on a classical idea of enriching the state space by artificially creating a filiation, in this context between orders of the book, which we believe has the potential of being useful for a broader class of models.

#### Article information

**Source**

J. Appl. Probab., Volume 51, Number 3 (2014), 625-639.

**Dates**

First available in Project Euclid: 5 September 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1409932663

**Digital Object Identifier**

doi:10.1239/jap/1409932663

**Mathematical Reviews number (MathSciNet)**

MR3256216

**Zentralblatt MATH identifier**

1305.60086

**Subjects**

Primary: 60J85: Applications of branching processes [See also 92Dxx]

Secondary: 60G55: Point processes

**Keywords**

Limit order book branching random walk branching random walk with a barrier

#### Citation

Simatos, Florian. Coupling limit order books and branching random walks. J. Appl. Probab. 51 (2014), no. 3, 625--639. doi:10.1239/jap/1409932663. https://projecteuclid.org/euclid.jap/1409932663