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.
Australian Research Council
Publication titleProceedings of the 9th International Conference on Matrix-Analytic Methods in Stochastic Models
EditorsQM He, G Horvath, M Telek
Department/SchoolSchool of Natural Sciences
Place of publicationBudapest, Hungary
Event title9th International Conference on Matrix-Analytic Methods in Stochastic Models
Event VenueBudapest, Hungary
Date of Event (Start Date)2016-06-28
Date of Event (End Date)2016-06-30
Rights statementCopyright unknown