Ergodicity and scaling limit of a constrained multivariate Hawkes process
By Ban Zheng, Franccois Roueff, Frédéric Abergel. 2013
52 citations recorded by the source corpus.
We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional constraint variable, whose evolution is driven by the point process. We study this process in the special case where the fertility function is exponential so that the process is entirely described by an underlying Markov chain, which includes the constraint variable. Some conditions on the parameters are established to ensure the ergodicity of the chain. Moreover, scaling limits are derived for the integrated point process. This study is primarily motivated by the stochastic modelling of a limit order book for high frequency financial data analysis.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/9dd243d6ea6f6bc4a04053b7ef9e15178b531fad
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In Applied Mathematics
- Fabrizio Lillo
- Simon Clinet
- Nakahiro Yoshida
- M. Rambaldi
- Emmanuel Bacry
- Alan G. Hawkes
- Mathieu Rosenbaum
- Jean-François Muzy
Citations in the corpus
- Hawkes Processes in Finance (2015, unknown): “Fitted Hawkes D Nt Contracts T dt Φ(t) Comments Section 2 [15] Bowsher 1-2 Trade Stocks 2 months 1s 2-Exp + seasonality [18] Chavez et al. 1 Extreme ∆P Stocks 1 year 1ms 2-Exp Marked [42] Jaisson et al. 8 Level-I Futures 1 year 1µs NP Section 3 [2] Bacry et al. 1 Trade Futures 3.5 months 1ms NP 2 Pr”
- Statistical inference for ergodic point processes and application to Limit Order Book (2015, background): “Lately, more complex dynamics have been studied, including Markovian models [11], Hawkes process driven bid-ask prices [3, 22], or even mixture of those approaches [2].”
- The role of volume in order book dynamics: a multivariate Hawkes process analysis (2016, background): “…linear specification (5) in favour of nonlinear formulations that ensure the positiveness of the intensity, while at the same time allowing the presence of negative valued kernels and thus inhibitory effects (Brémaud and Massoulié 1996, Sornette and Ouillon 2005, Bowsher 2007, Zheng et al. 2014).”