Approximation of exit times for one-dimensional linear diffusion processes
| Autor: | Samuel Herrmann, Nicolas Massin |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB) |
| Rok vydání: | 2020 |
| Předmět: |
Generalization
Order (ring theory) Context (language use) Exit time Random walk 010103 numerical & computational mathematics Stochastic algorithm 01 natural sciences Linear diffusion 010101 applied mathematics Computational Mathematics Computational Theory and Mathematics Diffusion process Position (vector) Modeling and Simulation Applied mathematics Generalized spheroids [MATH]Mathematics [math] 0101 mathematics Diffusion (business) Brownian motion Mathematics |
| Zdroj: | Computers & Mathematics with Applications Computers & Mathematics with Applications, Elsevier, 2020, 80 (6), pp.1668-1682. ⟨10.1016/j.camwa.2020.07.023⟩ |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2020.07.023 |
| Popis: | International audience; In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and the Ornstein-Uhlenbeck context, that is for particular time-homogeneous diffusion processes. Here the aim is therefore to generalize this efficient numerical approach in order to obtain an approximation of both the exit time and position for a general linear diffusion. The main challenge of such a generalization is to handle with time-inhomogeneous diffusions. The efficiency of the method is described with particular care through theoretical results and numerical examples. |
| Databáze: | OpenAIRE |
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