Controlled Filtered Poisson Processes
Filtered Poisson processes are used as models in various applications, in particular in statistical hydrology. In this paper, controlled filtered Poisson processes are considered. The aim is to minimize the expected time that the process will spend in the continuation region. The dynamic programming...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| author | Mario Lefebvre |
| author_facet | Mario Lefebvre |
| author_sort | Mario Lefebvre |
| collection | DOAJ |
| description | Filtered Poisson processes are used as models in various applications, in particular in statistical hydrology. In this paper, controlled filtered Poisson processes are considered. The aim is to minimize the expected time that the process will spend in the continuation region. The dynamic programming equation satisfied by the value function is derived. To obtain the value function, and hence the optimal control, a non-linear integro-differential equation must be solved, subject to the appropriate boundary conditions. Various cases for the size of the jumps are treated and explicit results are obtained. |
| format | Article |
| id | doaj-art-4ca49e48612f45759e70b13567e28e3c |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4ca49e48612f45759e70b13567e28e3c2025-01-24T13:40:02ZengMDPI AGMathematics2227-73902025-01-0113228410.3390/math13020284Controlled Filtered Poisson ProcessesMario Lefebvre0Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-Ville, Montréal, QC H3C 3A7, CanadaFiltered Poisson processes are used as models in various applications, in particular in statistical hydrology. In this paper, controlled filtered Poisson processes are considered. The aim is to minimize the expected time that the process will spend in the continuation region. The dynamic programming equation satisfied by the value function is derived. To obtain the value function, and hence the optimal control, a non-linear integro-differential equation must be solved, subject to the appropriate boundary conditions. Various cases for the size of the jumps are treated and explicit results are obtained.https://www.mdpi.com/2227-7390/13/2/284stochastic controldynamic programminghoming problemfirst-passage timeintegro-differential equation |
| spellingShingle | Mario Lefebvre Controlled Filtered Poisson Processes Mathematics stochastic control dynamic programming homing problem first-passage time integro-differential equation |
| title | Controlled Filtered Poisson Processes |
| title_full | Controlled Filtered Poisson Processes |
| title_fullStr | Controlled Filtered Poisson Processes |
| title_full_unstemmed | Controlled Filtered Poisson Processes |
| title_short | Controlled Filtered Poisson Processes |
| title_sort | controlled filtered poisson processes |
| topic | stochastic control dynamic programming homing problem first-passage time integro-differential equation |
| url | https://www.mdpi.com/2227-7390/13/2/284 |
| work_keys_str_mv | AT mariolefebvre controlledfilteredpoissonprocesses |