Rates for branching particle approximations of continuous-discrete filters
| dc.creator | Kouritzin, Michael A. | |
| dc.creator | Sun, Wei | |
| dc.date | 2006-02-22 | |
| dc.date.accessioned | 2026-07-07T07:03:41Z | |
| dc.date.available | 2026-07-07T07:03:41Z | |
| dc.description | Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that $t\to X_t$ is a Markov process and we wish to calculate the measure-valued process $t\toμ_t(\cdot)\doteq P\{X_t\in \cdot|σ\{Y_{t_k}, t_k\leq t\}\}$, where $t_k=kε$ and $Y_{t_k}$ is a distorted, corrupted, partial observation of $X_{t_k}$. Then, one constructs a particle system with observation-dependent branching and $n$ initial particles whose empirical measure at time $t$, $μ_t^n$, closely approximates $μ_t$. Each particle evolves independently of the other particles according to the law of the signal between observation times $t_k$, and branches with small probability at an observation time. For filtering problems where $ε$ is very small, using the algorithm considered in this paper requires far fewer computations than other algorithms that branch or interact all particles regardless of the value of $ε$. We analyze the algorithm on Lévy-stable signals and give rates of convergence for $E^{1/2}\{\|μ^n_t-μ_t\|_γ^2\}$, where $\Vert\cdot\Vert_γ$ is a Sobolev norm, as well as related convergence results. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051605000000539 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0602488 | |
| dc.identifier | http://arxiv.org/abs/math/0602488 | |
| dc.identifier | Annals of Applied Probability 2005, Vol. 15, No. 4, 2739-2772 | |
| dc.identifier | doi:10.1214/105051605000000539 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109066 | |
| dc.subject | Probability | |
| dc.subject | 93E11 (Primary) 65C35 (Secondary) | |
| dc.title | Rates for branching particle approximations of continuous-discrete filters | |
| dc.type | text |