Pitman's 2M - X theorem for skip-free random walks with Markovian increments
Let (ξ k, k ≥ 0) be a Markov chain on {-1, +1} with ξ 0 = 1 and transition probabilities P(ξ k+1 = 1|ξ k = 1) = a and P(ξ k+1 = -1|ξ k = -1) = b < a. Set X 0 = 0, X n = ξ 1+⋯+ξ n and M n = max 0≤k≤n X k. We prove that the process 2M - X has the same law as that of X conditioned to stay non-ne...
| Main Authors: | , , |
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| Formato: | Journal article |
| Idioma: | English |
| Publicado em: |
2001
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| _version_ | 1826299284908146688 |
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| author | Hambly, B Martin, J O'Connell, N |
| author_facet | Hambly, B Martin, J O'Connell, N |
| author_sort | Hambly, B |
| collection | OXFORD |
| description | Let (ξ k, k ≥ 0) be a Markov chain on {-1, +1} with ξ 0 = 1 and transition probabilities P(ξ k+1 = 1|ξ k = 1) = a and P(ξ k+1 = -1|ξ k = -1) = b < a. Set X 0 = 0, X n = ξ 1+⋯+ξ n and M n = max 0≤k≤n X k. We prove that the process 2M - X has the same law as that of X conditioned to stay non-negative. |
| first_indexed | 2024-03-07T04:59:35Z |
| format | Journal article |
| id | oxford-uuid:d7d31e4d-8cf9-4c22-a6fd-4ed02cdff1a0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:59:35Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:d7d31e4d-8cf9-4c22-a6fd-4ed02cdff1a02022-03-27T08:43:46ZPitman's 2M - X theorem for skip-free random walks with Markovian incrementsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d7d31e4d-8cf9-4c22-a6fd-4ed02cdff1a0EnglishSymplectic Elements at Oxford2001Hambly, BMartin, JO'Connell, NLet (ξ k, k ≥ 0) be a Markov chain on {-1, +1} with ξ 0 = 1 and transition probabilities P(ξ k+1 = 1|ξ k = 1) = a and P(ξ k+1 = -1|ξ k = -1) = b < a. Set X 0 = 0, X n = ξ 1+⋯+ξ n and M n = max 0≤k≤n X k. We prove that the process 2M - X has the same law as that of X conditioned to stay non-negative. |
| spellingShingle | Hambly, B Martin, J O'Connell, N Pitman's 2M - X theorem for skip-free random walks with Markovian increments |
| title | Pitman's 2M - X theorem for skip-free random walks with Markovian increments |
| title_full | Pitman's 2M - X theorem for skip-free random walks with Markovian increments |
| title_fullStr | Pitman's 2M - X theorem for skip-free random walks with Markovian increments |
| title_full_unstemmed | Pitman's 2M - X theorem for skip-free random walks with Markovian increments |
| title_short | Pitman's 2M - X theorem for skip-free random walks with Markovian increments |
| title_sort | pitman s 2m x theorem for skip free random walks with markovian increments |
| work_keys_str_mv | AT hamblyb pitmans2mxtheoremforskipfreerandomwalkswithmarkovianincrements AT martinj pitmans2mxtheoremforskipfreerandomwalkswithmarkovianincrements AT oconnelln pitmans2mxtheoremforskipfreerandomwalkswithmarkovianincrements |