Onsager-Machlup functional for stochastic differential equations with time-varying noise
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929643009867776 |
|---|---|
| author | Zhang, Xinze Li, Yong |
| author_facet | Zhang, Xinze Li, Yong |
| contents | This paper is devoted to studying the Onsager-Machlup functional for stochastic differential equations with time-varying noise of the α-Hölder, 0<α<1/4, dXt =f(t,Xt)dt+g(t)dWt.
Our study focuses on scenarios where the diffusion coefficient g(t) exhibits temporal variability, starkly contrasting the conventional assumption of a constant diffusion coefficient in the existing literature. This variance brings some complexity to the analysis. Through this investigation, we derive the Onsager-Machlup functional, which acts as the Lagrangian for mapping the most probable transition path between metastable states in stochastic processes affected by time-varying noise. This is done by introducing new measurable norms and applying an appropriate version of the Girsanov transformation. To illustrate our theoretical advancements, we provide numerical simulations, including cases of a one-dimensional SDE and a fast-slow SDE system, which demonstrate the application to multiscale stochastic volatility models, thereby highlighting the significant impact of time-varying diffusion coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04290 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Onsager-Machlup functional for stochastic differential equations with time-varying noise Zhang, Xinze Li, Yong Probability 82C35, 60H10, 37H10 This paper is devoted to studying the Onsager-Machlup functional for stochastic differential equations with time-varying noise of the α-Hölder, 0<α<1/4, dXt =f(t,Xt)dt+g(t)dWt. Our study focuses on scenarios where the diffusion coefficient g(t) exhibits temporal variability, starkly contrasting the conventional assumption of a constant diffusion coefficient in the existing literature. This variance brings some complexity to the analysis. Through this investigation, we derive the Onsager-Machlup functional, which acts as the Lagrangian for mapping the most probable transition path between metastable states in stochastic processes affected by time-varying noise. This is done by introducing new measurable norms and applying an appropriate version of the Girsanov transformation. To illustrate our theoretical advancements, we provide numerical simulations, including cases of a one-dimensional SDE and a fast-slow SDE system, which demonstrate the application to multiscale stochastic volatility models, thereby highlighting the significant impact of time-varying diffusion coefficients. |
| title | Onsager-Machlup functional for stochastic differential equations with time-varying noise |
| topic | Probability 82C35, 60H10, 37H10 |
| url | https://arxiv.org/abs/2407.04290 |