Theory of Continuous Storage with Markov Additive Inputs and a General Release Rule.
Abstract
A continuous storage model is introduced where the release rate is given by an arbitrary continuous increasing function r and the input process Y has conditionally independent (in general non-stationary) increments given the paths of a Markov process X. Then the content process Z is defined by a stochastic integral equation. Its solution is obtained and shown to be a conditional Markov process defined on the Markov process X, and the two-dimensional process (X,Z) is almost a standard Markov process. Ergodic properties of Z are discussed in terms of the paramerers defining the input Y and necessary and sufficient conditions are given for the existence of proper limiting distributions in a special case of particular interest. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1972
- Accession Number
- AD0740107
Entities
People
- Erhan Cinlar
Organizations
- Stanford University