Generalised reward generator for stochastic fluid models
We construct a generalised reward matrix Z(s). which is an extension of the fluid generator Q(s) of a stochastic fluid model (SFM). We classify the generators that are projections of Z(s), including the generator Q(s), and discuss the application of the resulting generators in different contexts.
As one application example, for the case with nonzero mean drift, we derive a new Riccati equation for the key matrix Ψ, which records the probabilities of the first return to the original level.
The Riccati equation has the form Ψ + ΨM-+Ψ = M+-, where parameters M+- and M-+ are block matrices in the matrix M, which records the expected number of visits to the original level, before the unbounded fluid drifts to ± ∞.
Finally, we derive the explicit form Ψ = M+- (I + M--)-1.
Funding
Australian Research Council
History
Publication title
Proceedings of the 9th International Conference on Matrix-Analytic Methods in Stochastic ModelsEditors
QM He, G Horvath, M TelekPagination
27-34ISBN
9781450321389Department/School
School of Natural SciencesPublisher
ACMPlace of publication
Budapest, HungaryEvent title
9th International Conference on Matrix-Analytic Methods in Stochastic ModelsEvent Venue
Budapest, HungaryDate of Event (Start Date)
2016-06-28Date of Event (End Date)
2016-06-30Rights statement
Copyright unknownRepository Status
- Open