Control of Conditional Processes and Fleming--Viot Dynamics
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908597769732096 |
|---|---|
| author | Jettkant, Philipp |
| author_facet | Jettkant, Philipp |
| contents | We discuss equivalent formulations of the control of conditional processes introduced by Lions. In this problem, a controlled diffusion process is killed once it hits the boundary of a given domain and the controller's reward is computed based on the conditional distribution given the process's survival. So far there is no clarity regarding the relationship between the open- and closed-loop formulation of this nonstandard control problem. We provide a short proof of their equivalence using measurable selection and mimicking arguments. In addition, we link the closed-loop formulation to Fleming--Viot dynamics of McKean--Vlasov type, where upon being killed the diffusion process is reinserted into the domain according to the current law of the process itself. This connection offers a new interpretation of the control problem and opens it up to applications that feature costs caused by reinsertion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15195 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Control of Conditional Processes and Fleming--Viot Dynamics Jettkant, Philipp Probability We discuss equivalent formulations of the control of conditional processes introduced by Lions. In this problem, a controlled diffusion process is killed once it hits the boundary of a given domain and the controller's reward is computed based on the conditional distribution given the process's survival. So far there is no clarity regarding the relationship between the open- and closed-loop formulation of this nonstandard control problem. We provide a short proof of their equivalence using measurable selection and mimicking arguments. In addition, we link the closed-loop formulation to Fleming--Viot dynamics of McKean--Vlasov type, where upon being killed the diffusion process is reinserted into the domain according to the current law of the process itself. This connection offers a new interpretation of the control problem and opens it up to applications that feature costs caused by reinsertion. |
| title | Control of Conditional Processes and Fleming--Viot Dynamics |
| topic | Probability |
| url | https://arxiv.org/abs/2409.15195 |