Finite-time implications of relaxation times for stochastically monotone processes |
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| Authors: | David J Aldous |
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| Institution: | (1) Department of Statistics, University of California, 94720 Berkeley, CA, USA;(2) Present address: INSA Toulouse, Tou7louse, France |
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| Abstract: | Summary For a continuous-time finite state Markov process with stationary distribution  , it is well-known thatP
i
(X
t
=j)-
j
isO(e
- t
) ast  , for a certain . For a stochastically monotone process for which the reversed process is also stochastically monotone, one can obtain bounds valid for allt. Precisely,
![$$\sum\limits_i {\pi _j \mathop {\max |}\limits_j P_i } (X_t \leqq j) - \pi 0,j]| \leqq 2(\lambda t + 2)$$](/content/m725830m6070637t/440_2005_Article_BF01848136_TeX2GIFIE1.gif)
exp(-t). The proof exploits duality for stochastically monotone processes.Research supported by National Science Foundation Grant MCS 84-03239 |
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| Keywords: | |
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