Similarity Solutions of Partial Differential Equations in Probability
Two-dimensional diffusion processes are considered between concentric circles and in angular sectors. The aim of the paper is to compute the probability that the process will hit a given part of the boundary of the stopping region first. The appropriate partial differential equations are solved expl...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2011/689427 |
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| _version_ | 1832562735316992000 |
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| author | Mario Lefebvre |
| author_facet | Mario Lefebvre |
| author_sort | Mario Lefebvre |
| collection | DOAJ |
| description | Two-dimensional diffusion processes are considered between concentric circles and in angular sectors. The aim of the paper is to compute the probability that the process will hit a given part of the boundary of the stopping region first. The appropriate partial differential equations are solved explicitly by using the method of similarity solutions and the method of separation of variables. Some solutions are expressed as generalized Fourier series. |
| format | Article |
| id | doaj-art-5044bc094ae04944a864d70f201a1470 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-5044bc094ae04944a864d70f201a14702025-02-03T01:21:56ZengWileyJournal of Probability and Statistics1687-952X1687-95382011-01-01201110.1155/2011/689427689427Similarity Solutions of Partial Differential Equations in ProbabilityMario Lefebvre0Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, C.P. 6079, Succursale Centre-Ville, Montréal, QC, H3C 3A7, CanadaTwo-dimensional diffusion processes are considered between concentric circles and in angular sectors. The aim of the paper is to compute the probability that the process will hit a given part of the boundary of the stopping region first. The appropriate partial differential equations are solved explicitly by using the method of similarity solutions and the method of separation of variables. Some solutions are expressed as generalized Fourier series.http://dx.doi.org/10.1155/2011/689427 |
| spellingShingle | Mario Lefebvre Similarity Solutions of Partial Differential Equations in Probability Journal of Probability and Statistics |
| title | Similarity Solutions of Partial Differential Equations in Probability |
| title_full | Similarity Solutions of Partial Differential Equations in Probability |
| title_fullStr | Similarity Solutions of Partial Differential Equations in Probability |
| title_full_unstemmed | Similarity Solutions of Partial Differential Equations in Probability |
| title_short | Similarity Solutions of Partial Differential Equations in Probability |
| title_sort | similarity solutions of partial differential equations in probability |
| url | http://dx.doi.org/10.1155/2011/689427 |
| work_keys_str_mv | AT mariolefebvre similaritysolutionsofpartialdifferentialequationsinprobability |