Weighted $L_\infty$ Asymptotic Characterisation of Perturbed Autonomous Linear Ordinary and Stochastic Differential Equations: Part I -- ODEs
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910660036657152 |
|---|---|
| author | Appleby, John A. D. Lawless, Emmet |
| author_facet | Appleby, John A. D. Lawless, Emmet |
| contents | This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or decay estimates. Part I considers deterministic equations, and part II Itô-type stochastic differential equations. Results from part I are used to deal with deterministically and stochastically forced equations in the second part. Results apply to both scalar and multi-dimensional equations, and connect the asymptotic behaviour of time averages of the forcing terms on finite intervals with the growth or decay rate of the solution. Mainly, results deal with large perturbations, but some indications of how results extend to tackle subdominant perturbations are also sketched. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted $L_\infty$ Asymptotic Characterisation of Perturbed Autonomous Linear Ordinary and Stochastic Differential Equations: Part I -- ODEs Appleby, John A. D. Lawless, Emmet Classical Analysis and ODEs Probability 34A30, 34C11, 34D05, 34D08, 34D10, 34E10 This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or decay estimates. Part I considers deterministic equations, and part II Itô-type stochastic differential equations. Results from part I are used to deal with deterministically and stochastically forced equations in the second part. Results apply to both scalar and multi-dimensional equations, and connect the asymptotic behaviour of time averages of the forcing terms on finite intervals with the growth or decay rate of the solution. Mainly, results deal with large perturbations, but some indications of how results extend to tackle subdominant perturbations are also sketched. |
| title | Weighted $L_\infty$ Asymptotic Characterisation of Perturbed Autonomous Linear Ordinary and Stochastic Differential Equations: Part I -- ODEs |
| topic | Classical Analysis and ODEs Probability 34A30, 34C11, 34D05, 34D08, 34D10, 34E10 |
| url | https://arxiv.org/abs/2410.16421 |