{"ID":2894406,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.11294","arxiv_id":"2507.11294","title":"Markov approximation for controlled Hawkes Jump-Diffusions with general kernels","abstract":"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.","short_abstract":"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-dif...","url_abs":"https://arxiv.org/abs/2507.11294","url_pdf":"https://arxiv.org/pdf/2507.11294v1","authors":"[\"Mahmoud Khabou\",\"Mehdi Talbi\"]","published":"2025-07-15T13:20:45Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[\"Diffusion Model\"]","has_code":false}