Further Exponential Generalization of Pitman’s 2m-x Theorem
نویسنده
چکیده
We present a class of processes which enjoy an exponential analogue of Pitman’s 2M-X theorem, improving hence some works of H. Matsumoto and M. Yor.
منابع مشابه
Skip-free Random Walks with Markovian Increments
Let (ξk, k ≥ 0) be a Markov chain on {−1, +1} with ξ0 = 1 and transition probabilities P (ξk+1 = 1| ξk = 1) = a and P (ξk+1 = −1| ξk = −1) = b < a. Set X0 = 0, Xn = ξ1 + · · ·+ ξn and Mn = max0≤k≤n Xk. We prove that the process 2M − X has the same law as that of X conditioned to stay non-negative. Pitman’s representation theorem [19] states that, if (Xt, t ≥ 0) is a standard Brownian motion and...
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