Variance Decay Property for Filter Stability
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913405076504576 |
|---|---|
| author | Kim, Jin Won Mehta, Prashant G. |
| author_facet | Kim, Jin Won Mehta, Prashant G. |
| contents | This paper is concerned with the problem of nonlinear (stochastic) filter stability of a hidden Markov model (HMM) with white noise observations. A contribution is the variance decay property which is used to conclude filter stability. For this purpose, a new notion of the Poincaré inequality (PI) is introduced for the nonlinear filter. PI is related to both the ergodicity of the Markov process as well as the observability of the HMM. The proofs are based upon a recently discovered minimum variance duality which is used to transform the nonlinear filtering problem into a stochastic optimal control problem for a backward stochastic differential equation (BSDE). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12850 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Variance Decay Property for Filter Stability Kim, Jin Won Mehta, Prashant G. Optimization and Control Probability This paper is concerned with the problem of nonlinear (stochastic) filter stability of a hidden Markov model (HMM) with white noise observations. A contribution is the variance decay property which is used to conclude filter stability. For this purpose, a new notion of the Poincaré inequality (PI) is introduced for the nonlinear filter. PI is related to both the ergodicity of the Markov process as well as the observability of the HMM. The proofs are based upon a recently discovered minimum variance duality which is used to transform the nonlinear filtering problem into a stochastic optimal control problem for a backward stochastic differential equation (BSDE). |
| title | Variance Decay Property for Filter Stability |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2305.12850 |