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...
| Hlavní autoři: | , , |
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
2001
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