Filtering of Stochastic Nonlinear Wave Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909549885128704 |
|---|---|
| author | Sritharan, Sivaguru S. Mudaliar, Saba |
| author_facet | Sritharan, Sivaguru S. Mudaliar, Saba |
| contents | In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider both stochastic calculus and white noise filtering methods and derive measure-valued evolution equations for the nonlinear filter and prove existence and uniqueness theorems for the solutions. We will also study first order approximations to these measure-valued evolutions by linearizing the wave equations and characterize the filter dynamics in terms of infinite dimensional operator Riccati equations and establish solvability theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18222 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Filtering of Stochastic Nonlinear Wave Equations Sritharan, Sivaguru S. Mudaliar, Saba Analysis of PDEs Mathematical Physics Functional Analysis Probability 35 Q40, 35Q61, 60 G35 In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider both stochastic calculus and white noise filtering methods and derive measure-valued evolution equations for the nonlinear filter and prove existence and uniqueness theorems for the solutions. We will also study first order approximations to these measure-valued evolutions by linearizing the wave equations and characterize the filter dynamics in terms of infinite dimensional operator Riccati equations and establish solvability theorems. |
| title | Filtering of Stochastic Nonlinear Wave Equations |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis Probability 35 Q40, 35Q61, 60 G35 |
| url | https://arxiv.org/abs/2503.18222 |