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math.PR2025
Some limit theorems for locally stationary Hawkes processes
Thomas Deschatre, Pierre Gruet, Antoine Lotz
We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties…
math.PR2021
On the control of the difference between two Brownian motions: an application to energy markets modeling
Thomas Deschatre
We derive a model based on the structure of dependence between a Brownian motion and its reflection according to a barrier. The structure of dependence presents two states of corre…
math.PR2016
On the control of the difference between two Brownian motions: a dynamic copula approach
Thomas Deschatre
We propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Bro…