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4135. On the Deviation matrix of an ergodic denumerable Markov process in continuous time with applications
Invited abstract in session MD-40: Stochastic Modelling, stream Advances in Stochastic Modelling and Learning Methods.
Monday, 14:30-16:00Room: 96 (building: 306)
Authors (first author is the speaker)
| 1. | Flora Spieksma
|
| Universiteit Leiden |
Abstract
The deviaton matrix is a measure of the cumulative deviation from the limiting probabilities and plays an important role in e.g. Markov (decision) processes, perturbed Markov processes, queueing theory,
and network centralities. It is well-known that the deviation matrix in the irreducible case exists if and only if the second moment of the return time from a fixed state to iself is finite.
We provide a necessary and sufficient condition for the deviation matrix to exist in the form of a system of two nested Lyapunov functions, the equivalent of which has been known for a long time for discrete time Markov chains.
However, it has not been realised earlier that finiteness of the deviation matrix implies that the absolute cumulative deviation from the limiting probabilities is finite as well. There is a relatively simple (but not simply proved) argument why this is true.
We further present a formula for the deviation matrix in terms of a rank one perturbation of the q-matrix.
We will illustrate our results with some applications
Keywords
- Stochastic Models
- Programming, Dynamic
Status: accepted
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