Yaglom limits can depend on the starting state
Event details
| Date | 11.03.2015 |
| Hour | 11:15 › 12:15 |
| Speaker | Prof. David McDonald, U. of Ottawa |
| Location | |
| Category | Conferences - Seminars |
When Keynes said, "in the long run we are all dead" he meant a transient description of a stochastic process is often more useful than a steady state analysis. For a Markov process with absorption it is clearly of interest to predict the state of the system at time n given it is still alive at time n. For an irreducible Markov kernel K on a finite state space S, it follows from the Perron-Frobenius theorem that, conditioned on being alive at time n, the distribution of the system tends to the Yaglom limit, the positive unit-norm right-eigenvector of K. In contrast, for countable state spaces a Yaglom limit may exist but it can depend on the initial state.
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- Jean-Yves Le Boudec