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Perfect sampling of non-monotonic Markov chains on infinite state space
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2019 |
| Abstract | In the modeling and analysis of discrete-events dynamical random systems, a first natural and crucial step consists in determining the stability region of the system, that is, the set of parameters guaranteeing that a stochastic process representing the state of the system (typically, a Markov chain) does not “explode” in the long run, and reaches an equilibrium. Second, one aims at characterizing this steady state by computing it, or at least, approximating it or simulating this stationary behavior. It is well known since the pioneering works of Borovkov and Foss [2, 3], and then Propp and Wilson [9] that coupling-from-the-past (CFTP) convergence can be a powerful tool for studying the asymptotic behavior of ergodic Markov chains. The so-called backwards schemes consist of a construction of the stationary state of the chain by initiating the recursion further and further away in the past, and keeping track of its value at the origin. This is a convergence to stationarity in a strong sense, and in this case the limit can be constructed explicitly as an almost sure limit on a suitable probability space. This can have many fruitful features, when it comes to comparing systems at equilibrium, via an adequate stochastic ordering of the corresponding chains, for instance. Further, in many cases where the stationary probability of the chain can be derived in closed form and/or its normalizing constant is not tractable, CFTP convergence is a powerful tool for perfectly sampling the stationary measure, that, is deriving an algorithmic procedure yielding to a sample drawn from the stationary measure itself. These techniques are at the core of the present PhD proposal. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.iecl.univ-lorraine.fr/Documents/SujetThesePefectSampleFinal.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
