On Carathéodory approximate scheme for a class of one-dimensional doubly perturbed diffusion processes
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929682952224768 |
|---|---|
| author | Belfadli, R. Boulanba, L. Ouknine, Y. |
| author_facet | Belfadli, R. Boulanba, L. Ouknine, Y. |
| contents | In this paper, we introduce and study the convergence of new Carathéodory's approximate solution for one-dimensional $α, β$-doubly perturbed stochastic differential equations (DPSDEs) with parameters $α<1$ and $β<1$ such that $|ρ| < 1$, where $ ρ: = \frac{αβ}{(1-α)(1-β)}$. Under Lipschitz's condition on the coefficients, we establish the $L^{p}$-convergence of the Carathéodory approximate solution uniformly in time, for all $p\geq 2$. As a consequence, and relying only on our scheme, we obtain the existence and uniqueness of strong solution for $α, β$-DPSDEs. Furthermore, an extension to non-Lipschitz coefficients are also studied. Our results improve earlier work by Mao and al. (2018). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Carathéodory approximate scheme for a class of one-dimensional doubly perturbed diffusion processes Belfadli, R. Boulanba, L. Ouknine, Y. Probability 60H10 (Primary) 60H35, 60J60 (Secondary) In this paper, we introduce and study the convergence of new Carathéodory's approximate solution for one-dimensional $α, β$-doubly perturbed stochastic differential equations (DPSDEs) with parameters $α<1$ and $β<1$ such that $|ρ| < 1$, where $ ρ: = \frac{αβ}{(1-α)(1-β)}$. Under Lipschitz's condition on the coefficients, we establish the $L^{p}$-convergence of the Carathéodory approximate solution uniformly in time, for all $p\geq 2$. As a consequence, and relying only on our scheme, we obtain the existence and uniqueness of strong solution for $α, β$-DPSDEs. Furthermore, an extension to non-Lipschitz coefficients are also studied. Our results improve earlier work by Mao and al. (2018). |
| title | On Carathéodory approximate scheme for a class of one-dimensional doubly perturbed diffusion processes |
| topic | Probability 60H10 (Primary) 60H35, 60J60 (Secondary) |
| url | https://arxiv.org/abs/2501.10036 |