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On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes

Please always quote using this URN: urn:nbn:de:bvb:20-opus-147819
  • A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- andA framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.show moreshow less

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Metadaten
Author: Beatrice Gaviraghi, Andreas Schindele, Mario Annunziato, Alfio Borzì
URN:urn:nbn:de:bvb:20-opus-147819
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Language:English
Parent Title (English):Applied Mathematics
Year of Completion:2016
Volume:7
Issue:16
Source:Applied Mathematics , 7, 1978-2004. http://dx.doi.org/10.4236/am.2016.716162
DOI:https://doi.org/10.4236/am.2016.716162
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 519 Wahrscheinlichkeiten, angewandte Mathematik
Tag:jump-diffusion processes; nonsmooth optimization; optimal control theory; partial integro-differential Fokker-Planck Equation; proximal methods
Release Date:2017/05/19
First Page:1978
Last Page:2004
EU-Project number / Contract (GA) number:304617
OpenAIRE:OpenAIRE
Collections:Open-Access-Publikationsfonds / Förderzeitraum 2016
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung