Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--Oregon State University, 1991. / Typescript (photocopy). Includes bibliographical references (leaves 71-73). Also available on the World Wide Web.

Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Thesis (M.S. in Operations Research)--Naval Postgraduate School, June 2005. / Thesis Advisor(s): Roberto Szechtman. Includes bibliographical references (p. 67-70). Also available online.

No description available.

We characterize the equilibrium behavior of a class of stochastic particle systems, where particles (representing customers, jobs, animals, molecules, etc.) enter a space randomly through time, interact, and eventually leave. The results are useful for analyzing the dynamics of randomly evolving systems including spatial service systems, species populations, and chemical reactions. Such models with interactions arise in the study of species competitions and systems where customers compete for service (such as wireless networks). The models we develop are space-time measure-valued Markov processes. Specifically, particles enter a space according to a space-time Poisson process and are assigned independent and identically distributed attributes. The attributes may determine their movement in the space, and whenever a new particle arrives, it randomly deletes particles from the system according to their attributes. Our main result establishes that spatial Poisson processes are natural temporal limits for a large class of particle systems. Other results include the probability distributions of the sojourn times of particles in the systems, and probabilities of numbers of customers in spatial polling systems without Poisson limits.

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Apresentamos um modelo estocástico para evolução de espécies utilizando processos de Poisson. Eventos de surgimento de novas espécies e eventos de extinção são dados por dois processos de Poisson independentes. A cada evento de surgimento, uma nova espécie é adicionada ao sistema e uma aptidão aleatória é associada a ela. À cada evento de extinção, é associado um limiar também aleatório e todas as espécies com aptidão inferior ao limiar são retiradas do sistema. Apresentamos critérios necessários e suficientes para recorrência/transitoriedade da configuração vazia. Mostramos a existência da distribuição limite e apresentamos critérios necessários e suficientes para um número in/finito de espécies em tal distribuição. / We present a stochastic model for species evolution based on Poisson Processes. Birth of new species and extinction events are given by two independent Poisson processes. At each birth, a new species enters the system and is given a random fitness mark. To each extinction event is associated a random threshold mark and all species with fitness lower than the threshold are removed from the system. We present necessary and suficient criteria for the recurrence/transience of the empty configuration. We show the existence of the limit distribution and present necessary and suficient criteria for an in/finite number os species in such distribution.

This dissertation studies information acquisition when the choice of information is fully flexible. Throughout the dissertation, I consider a theoretical framework where a decision maker (DM) acquires costly information (signal process) about the payoffs of different alternatives before making a choice. In Chapter 1, I solve a general model where the DM pays a cost that depends on the rate of uncertainty reduction and discounts delayed payoffs. The main finding is that the optimal signal process resembles a Poisson signal --- the signal arrives occasionally according to a Poisson process, and it drives the inferred posterior belief to jump discretely. The optimal signal is chosen to confirm the DM's prior belief of the most promising state. Once seeing the signal, the decision maker is discretely surer about the state and stops learning immediately. When the signal is otherwise absent, the decision maker becomes gradually less sure about the state, and continues learning by seeking more precise but less frequently arriving signals. In Chapter 2, I study the sequential implementation of a target information structure. I characterize the set of decision time distributions induced by all signal processes that satisfy a per-period learning capacity constraint on the rate of uncertainty reduction. I find that all decision time distributions have the same mean, and the maximal and minimal elements by mean-preserving spread order are exponential distribution and deterministic distribution. The result implies that when the time preference is risk loving (e.g. standard or hyperbolic discounting), Poisson signal is optimal since it induces the riskiest exponential decision time distribution. When time preference is risk neutral (e.g. constant delay cost), all signal processes are equally optimal. In Chapter 3, I relax the assumption on information cost by assuming that the measure of signal informativeness is an indirect measure from sequential minimization. I first show that an indirect information measure is supported by sequential minimization iff it satisfies: 1) monotonicity in Blackwell order, 2) sub-additivity in compound experiments and 3) linearity in mixing with no information. Then I study a dynamic information acquisition problem where the cost of information depends on an indirect information measure and the delay cost is fixed (the DM is time-risk neutral). The optimal strategy is to acquire Poisson type signals. The result implies that when the cost of information is measured by an indirect measure, Poisson signals are intrinsically cheaper than other signal processes. Chapter 4 introduces a set of useful technical results on constrained information design that is used to derive the main results in the first three chapters.

Apresentamos um modelo estocástico para evolução de espécies utilizando processos de Poisson. Eventos de surgimento de novas espécies e eventos de extinção são dados por dois processos de Poisson independentes. A cada evento de surgimento, uma nova espécie é adicionada ao sistema e uma aptidão aleatória é associada a ela. À cada evento de extinção, é associado um limiar também aleatório e todas as espécies com aptidão inferior ao limiar são retiradas do sistema. Apresentamos critérios necessários e suficientes para recorrência/transitoriedade da configuração vazia. Mostramos a existência da distribuição limite e apresentamos critérios necessários e suficientes para um número in/finito de espécies em tal distribuição. / We present a stochastic model for species evolution based on Poisson Processes. Birth of new species and extinction events are given by two independent Poisson processes. At each birth, a new species enters the system and is given a random fitness mark. To each extinction event is associated a random threshold mark and all species with fitness lower than the threshold are removed from the system. We present necessary and suficient criteria for the recurrence/transience of the empty configuration. We show the existence of the limit distribution and present necessary and suficient criteria for an in/finite number os species in such distribution.