Central Limit Theorem for a Partially Observed Interacting System of Hawkes Processes I: Subcritical Case

Battle Count: 56

Hawkes processes are widely used in quantitative finance for modeling high-frequency trading events, order book dynamics, and market microstructure noise. This paper's theoretical results on parameter estimation for interaction probabilities could inform models of cascading events in financial markets. However, the paper is purely theoretical with no direct trading applications, no empirical validation, and focuses on the subcritical regime. The mean-field scaling and partial observation framework could be relevant for modeling large-scale financial systems where only a subset of agents is observable.

This is a highly advanced theoretical mathematics paper requiring deep expertise in stochastic processes, martingale theory, random matrix theory, and asymptotic statistics. The proofs span 56+ pages with extensive technical lemmas. There is no computational implementation - the paper establishes theoretical guarantees. Reproducing the results requires verifying complex mathematical arguments involving multiple decomposition schemes, Burkholder-Davis-Gundy inequalities, and Jacod-Shiryaev martingale CLT conditions.

This is a pure theoretical mathematics paper with complete proofs provided in the main text and appendices. All lemmas, theorems, and their proofs are fully detailed. The mathematical arguments are self-contained given the referenced prior works [13] and [21]. No computational experiments are needed for verification - correctness is established through rigorous mathematical proof. The only limitation is the reliance on results from prior papers [13] and [21] for some auxiliary lemmas.