Ergodicity and scaling limit of a constrained multivariate Hawkes processReport as inadecuate

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* Corresponding author 1 FiQuant - Chaire de finance quantitative 2 LTCI - Laboratoire Traitement et Communication de l-Information 3 MAS - Mathématiques Appliquées aux Systèmes - EA 4037

Abstract : 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.

Keywords : Point processes Hawkes processes Limit theorems Discretisation of stochastic processes limit order book

Author: Ban Zheng - François Roueff - Frédéric Abergel -



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