Semi-Markov representations of some stochastic point processes

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A limitation of Markov representation for stationary processes

AbstractThe existence of a representation of a stationary process as an instantaneous function of a real, irreducible Markov chain (Harris chain) imposes important restrictions on the distribution of the process. We construct a countably-valued stationary process with a very strong mixing property for which such a representation does not exist

REDUCTION OF STATE VARIABLE DIMENSION IN STOCHASTIC DYNAMIC OPTIMIZATION MODELS WHICH USE TIME-SERIES DATA

Statistical procedures are developed for reducing the number of autonomous state variables in stochastic dynamic optimization models when these variables follow a stationary process over time. These methods essentially delete part of the information upon which decisions are based while maintaining a logically consistent model. The relatively simple linear autoregressive process as well as the general case is analyzed and the necessary formulae for practical application are derived. Several applications in agricultural economics are discussed and results presented which quantify the relative amount of information sacrificed with the reduction in number of state variables.Research Methods/ Statistical Methods,

Crossings states and sets of states in P\'olya random walks

We consider the P\'olya random walk in $\mathbb{Z}^2$. The paper establishes a number of results for the distributions and expectations of the number of usual (undirected) and specifically defined in the paper up- and down-directed state-crossings and different sets of states crossings. One of the most important results of this paper is that the expected number of undirected state-crossings $\mathbf{n}$ is equal to 1 for any state $\mathbf{n}\in\mathbb{Z}^2\setminus\{\mathbf{0}\}$. As well, the results of the paper are extended to $d$-dimensional random walks, $d\geq2$, in bounded areas.Comment: Dear readers. I made a tremendous work to revise this paper after referee report. There are 30 pages of 11pt format, 4 figures and 1 tabl

Protocol engineering from Estelle specifications

Bibliography: leaves 129-132.The design of efficient, reliable communication protocols has long been an area of active research in computer science and engineering, and will remain so while the technology continues to evolve, and information becomes increasingly distributed. This thesis examines the problem of predicting . the performance of a multi-layered protocol system directly from formal specifications in the ISO specification language Estelle, a general-purpose Pascal-based language with support for concurrent processes in the form of communicating extended finite-state machines. The thesis begins with an overview of protocol engineering, and a discusses the areas of performance evaluation and protocol specification. Important parts of the mathematics of discrete-time semi-Markov processes are presented to assist in understanding the approaches to performance evaluation described later. Not much work has been done to date in the area of performance prediction from specifications. The idea was first mooted by Rudin, who illustrated it with a simple model based on the global state reachability graph of a set of synchronous communicating FSMs. About the same time Kritzinger proposed a closed multiclass queueing model. Both of these approaches are described, and their respective strengths and weaknesses pointed out. Two new methods are then presented. They have been implemented as part of an Estelle-based CASE tool, the Protocol Engineering Workbench (PE!V). In the first approach, we show how discrete-time semi-Markov chain models can be derived from meta-executions of Estelle specifications, and consider ways of using these models predictively. The second approach uses a structure similar to a global-state graph. Many of the limitations of Rudin's approach are overcome, and our technique produces highly accurate performance predictions. The PEW is also described in some detail, and its use in performance evaluation illustrated with some examples. The thesis concludes with a discussion of the strengths and weaknesses of the new methods, and possible ways of improving them