# Markov approximation for controlled Hawkes Jump-Diffusions with general kernels

arXiv: https://arxiv.org/abs/2507.11294 · HTML: https://mlsanity.com/paper/2507.11294/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2025.

## Built on by (most cited first, 2 of 2)

- [Continuous-Time Reinforcement Learning for Controlled Hawkes Jump-Diffusions](https://mlsanity.com/paper/2608.19151/) (2026)
- [When Should a Human Take Back Control? Optimal Delegation under Turbulent AI Risk](https://mlsanity.com/paper/2609.32083/) (2026)

## Abstract (arXiv)

We present a Markov approximation for jump-diffusions whose jump part consists in a Hawkes process with intensity driven by a general (possibly non-monotone) kernel. Under minimal integrability conditions, the kernel can be approximated by a linear combination of exponential functions. This implies that Hawkes jump-diffusions can be approximated with Markov jump-diffusions. We illustrate the usefulness of this approximation by applying it to a class of stochastic control problems.