The hybrid exact scheme for the simulation of first-passage times of jump-diffusions with time-dependent thresholds
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915589406064640 |
|---|---|
| author | Desmettre, Sascha Khurana, Devika Meddah, Amira |
| author_facet | Desmettre, Sascha Khurana, Devika Meddah, Amira |
| contents | The first-passage time is a key concept in stochastic modeling, representing the time at which a process first reaches a specified threshold. In this work, we consider a jump-diffusion (JD) model with a time-dependent threshold, providing a more flexible framework for describing stochastic dynamics. We are interested in the Exact simulation method developed for JD processes with constant thresholds, where the Exact method for pure diffusion is applied between jump intervals. An adaptation of this method to time-dependent thresholds has recently been proposed for a more general stochastic setting. We show that this adaptation can be applied to JD models by establishing a formal correspondence between the two frameworks. A comparative analysis is then performed between the proposed approach and the constant-threshold version in terms of algorithmic structure and computational efficiency. Finally, we show the applicability of the method by predicting neuronal spike times in a JD model driven by two independent Poisson jump mechanisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The hybrid exact scheme for the simulation of first-passage times of jump-diffusions with time-dependent thresholds Desmettre, Sascha Khurana, Devika Meddah, Amira Statistical Mechanics Probability 37M05, 65C20, 60G05, 60H35, 92C20 The first-passage time is a key concept in stochastic modeling, representing the time at which a process first reaches a specified threshold. In this work, we consider a jump-diffusion (JD) model with a time-dependent threshold, providing a more flexible framework for describing stochastic dynamics. We are interested in the Exact simulation method developed for JD processes with constant thresholds, where the Exact method for pure diffusion is applied between jump intervals. An adaptation of this method to time-dependent thresholds has recently been proposed for a more general stochastic setting. We show that this adaptation can be applied to JD models by establishing a formal correspondence between the two frameworks. A comparative analysis is then performed between the proposed approach and the constant-threshold version in terms of algorithmic structure and computational efficiency. Finally, we show the applicability of the method by predicting neuronal spike times in a JD model driven by two independent Poisson jump mechanisms. |
| title | The hybrid exact scheme for the simulation of first-passage times of jump-diffusions with time-dependent thresholds |
| topic | Statistical Mechanics Probability 37M05, 65C20, 60G05, 60H35, 92C20 |
| url | https://arxiv.org/abs/2511.00155 |