Optimal response for stochastic differential equations by local kernel perturbations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910974617845760 |
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| author | del Sarto, Gianmarco Galatolo, Stefano Jain, Sakshi |
| author_facet | del Sarto, Gianmarco Galatolo, Stefano Jain, Sakshi |
| contents | We consider a random dynamical system on $\mathbb{R}^d$, whose dynamics is defined by a stochastic differential equation. The annealed transfer operator associated with such systems is a kernel operator. Given a set of feasible infinitesimal perturbations $P$ to this kernel, with support in a certain compact set, and a specified observable function $ϕ: \mathbb{R}^d \to \mathbb{R}$, we study which infinitesimal perturbation in $P$ produces the greatest change in expectation of $ϕ$. We establish conditions under which the optimal perturbation uniquely exists and present a numerical method to approximate the optimal infinitesimal kernel perturbation. Finally, we numerically illustrate our findings with concrete examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09300 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal response for stochastic differential equations by local kernel perturbations del Sarto, Gianmarco Galatolo, Stefano Jain, Sakshi Dynamical Systems Optimization and Control 37H05, 37H30, 47B34, 82C31, 93E03 We consider a random dynamical system on $\mathbb{R}^d$, whose dynamics is defined by a stochastic differential equation. The annealed transfer operator associated with such systems is a kernel operator. Given a set of feasible infinitesimal perturbations $P$ to this kernel, with support in a certain compact set, and a specified observable function $ϕ: \mathbb{R}^d \to \mathbb{R}$, we study which infinitesimal perturbation in $P$ produces the greatest change in expectation of $ϕ$. We establish conditions under which the optimal perturbation uniquely exists and present a numerical method to approximate the optimal infinitesimal kernel perturbation. Finally, we numerically illustrate our findings with concrete examples. |
| title | Optimal response for stochastic differential equations by local kernel perturbations |
| topic | Dynamical Systems Optimization and Control 37H05, 37H30, 47B34, 82C31, 93E03 |
| url | https://arxiv.org/abs/2502.09300 |