MARKOV PROCESSES

Author: PUERTO GARCÍA INÉS M. DEL.
Year: 2002.
University: EXTREMADURA [www.unex.es].
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This dissertation is framed within the General Theory on branching processes of Galton-Watson, focusing on family processes Galton-Watson controlled. Specifically, it has made contributions to the theory of a probabilistic model Galton-Watson controlled random theory and inferential a model Galton-Watson controlled deterministic control. It is structured into five chapters, some conclusions and some questions for future research. In chapter 1, introductory in nature, provides an overview of the models which are branching class processes Galton-Watson controlled and the main problems that they have been investigated hata this time. Chapters 2, 3 and 4 are devoted to the study process Galton-Watson controlled random hash function. In particular, in Chapter 2, as the process Gaton-Watson with random hash function is a Markov chain with stationary probability of transition, establishing results for the communication between their states and the classification of the same, leaving certain relations between the probability generating functions associated with variables aletatorias involved in the process. From them, you get the main moments both conditional and non-conditional process. Finally, we provide results for the progeny accumulated to a certain generation No $ $. In Chapter 3, lays down conditions under which the process is extinguished with a probability conditions and guaranteeing their extinction not likely positive. It is also proposed a classification, Chapter 4, focuses on the study of behavior limit conveniently standardized process. Specifically in the supercritical case was investigated conditions necessary and / or sufficient to guarantee a geometric growth in the process. This study is carried out considering three possible types of convergence: the convergence almost certainly, at $ L ^ $ 1 and $ L ^ 2 $. In the case establishing the critical convergence in distribution process nomalizado $ $ No to a mixture of a degenerate distribution at the point 0 and distribujción belonging to the family Gamma obtained, therefore, a linear growth process. Finally, for subcritical and processes under the assumption that 0 is not a state absorbent, we obtain convergence in law to distribuicón stationary in the chain. In chapter 5, addresses the theory inference for a process Galton-Watson controlled controlled fixed. Under non - parametric context, and considering various options for the sample information are proposed estimators for parameters for the model (the possibilities, average and variance associated with the act of reproduction process) and their properties are investigated to determine its moments (conditional and untied), consistency (weak and strong) the same and sets its limits conveniently standard distributions. From study of the properties of consistency and normalcy asymptotic, providing confidence intervals for the parameters studied. As an illustration, we provide some examples in which simulated reflected the strong performance of estimators obtained.

Author: RAMOS CANTARIÑO ALFONSO.
Year: 2002.
University: EXTREMADURA [www.unex.es].
Place of defense: ESCUELA POLITÉCNICA DE CÁCERES.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This teis doctoral is framed within the General Theory on branching processes of Galton-Watson, focusing on family procesod and Galton-Watson bisexual. Specifically, it has made contributions to the theory of probability two new models Galton-Watson bisexual, process Galton-Watson bisexual with mating dependent on the size of the population and the process of Galton-Watson bisexual environment variable. It is structured into three chapters, some conclusions and some questions for future research. In chapter 1, introductory in nature, provides an overview of the models which are branching class processes Galton-Watson bisexuals and the major problems that they have been investigated until this moment. Chapters 2 and 3 are devoted to the study of the two new models introduced bisexual. In particular, in Chapter 2, we introduce the model with bisexual mating dependent on the size of the population. After completing their probabilistic description, that is a Markov chain with stationary transition probabilities, we determine a set of relationships among the functions generatirces probability associated with the random variables involved in the model and, based on these relationships, we get the main points in the process. In a next step, we provide conditions under which occurs extinction process with probability 1 and conditions that guarantee its extinction not likely positive, and low status of non-extinction, we study results on the convergence almost certainly, at $ L ^ $ 1 and $ L ^ 2 $, in the process, conveniently standardized to some random variable limit fínita and not degenerate to zero. Finally, we get some results for his progeny accumulated to a certain generation. In chapter 3, we introduce our second model, the so-called model bisexual environment variable, which allows for the possibility that the probability distribution that governs reproduction of the process, not the same in all generations. Similar to the methodology used in the previous model is considered for the study of this new model, with the exception of the results for his progeny accumulated, whose study, the same as for PGW asexual environment variable involves great difficulty. In addition to the three chapters commented, also included a section in which, by way of summary, we provide some final conclusions and some questions open for future research.

Author: MARTÍNEZ QUINTANA RODRIGO.
Year: 2003.
University: EXTREMADURA [www.unex.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This dissertation is framed within the General Theory on branching processes of Galton-Watson, focusing on family processes branching Multitipo. It raises essentially the introduction of a new model that allows us to study in a unified manner to a major class of processes branching Multitipo Homogéneos. In this model has been called Process branching Multitipo Generalized Depending on the size of the population. The thesis has been structured into six chapters, some final conclusions and some questions for future research and some appendices. In Chapter 1, a introductorío, provides an overview of the process branching Multitipo as well as changes Depending on the size of the population and controlled, and the major problems in relation to them have been investigated until now time. In Chapter 2 introduces the process of branching Multitipo Generalized Depending on the size of the population. After completing its definition and interpretation íntuitiva, it is found that is a string of Markov multitipo homogeneous results for establishing communication between their states and the classification of the same and get the key moments conditional process. In Chapters 3, 4 and 5 are considered studying the probability of extinction and behavioral limit, first under the more general context of a Markov Chain Homogeneous, then particularize lós results Process branching Multitipo Generalized Depending on the size of the population. More specifically, in Chapter 3 defines conditions under which the chain was extinguished with a probability conditions and guaranteeing their extinction not likely positive. Besides proposing a classification of the same which distinguishes between cases subcritical, critical and supercritical, following basically the behavioral differences in terms of extinction. Based on this classification, Chapters 4 and 5 are. Dedicated to the study of critical and supercritical cases respectively. In these chapters he examines the behavior of the chain limit conveniently and standardized functional associated with the same linear, providing results on the convergence almost certainly, Lr for 1mayor-mayor2, probability and distribution to limits not degenerate to zero and finite. In Chapter 6, apply the results obtained in previous chapters to individual cases Process branching Multitipo Modified. More specifically consider new models that extend the process branching Multitipo Depending on the size of the population and the process of branching Multitipo controlled, which have not been studied so far, and which have been called processes with branching Multitipo Controlled Random Control and Reproduction Depending on the size of the population. This application shows the power of the techniques developed over the thesis.

Author: MARTÍNEZ QUINTANA RODRIGO.
Year: 2003.
University: EXTREMADURA [www.unex.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This dissertation is framed within the General Theory About branching processes of Galton-Watson, focusing on family processes branching Multitipo. It raises essentially the introduction of a new model that allows us to study in a unified manner to a major class of processes branching Multitipo homogeneous. In this model has been called Process branching Multitipo Generalized dependent on the size of the population. The thesis is structured in 6 chapters, some final conclusions and some questions for future research and some appendices. In Chapter 1, introductory in nature, provides an overview of the process branching Multitipo as well as changes Dependent Size of Population and controlled, and the major problems in relation to them have been investigated until now time. In Chapter 2 introduces the process of branching Multitipo Generalized dependent on the population size. After completing its definition and interpretation intuitive, it is found that is a string of Markov mulititpo homogeneous sets results for the communication between their states and the classification of the same and get the key moments conditional process. In Chapters 3, 4 and 5 are considered studying the probability of extinction and behavioral limit, first under the more general context of a Markov Chain Homogeneous, then particularize results Process branching Multitipo Generalized Depending on the size of the population. More specifically, Chapter 3 defines conditions under which the chain was extinguished with a probability conditions and guaranteeing their extinction not likely positive. It is also proposed a classification of the same which distinguishes between cases subcritical, critical and supercritical, following basically the behavioral differences in terms of extinction. Based on this classification, Chapters 4 and 5 dedicated to the study of critical and supercritical cases respectively. In these chapters he examines the behavior of the chain limit conveniently and standardized functional associated with the same linear, providing results on the convergence almost certainly, Lr for 1 minor r lesser 2, and probability distribution to limits not degenerate into zero and finite. In Chapter 6, apply the results obtained in previous chapters to individual cases Process branching Multitipo Modified. More specifically consider new models that extend the process branching Multitipo Depending on the size of the population and the process of branching Multitipo controlled, which have not been studied so far, and which have been called processes with branching Multitipo Controlled Random Control and Reproduction Depending on the size of the population. This application shows the power of the techniques developed over the thesis.

Author: Zaragoza Ramírez M.Alba.
Year: 2006.
University: LLEIDA [www.udl.es].
Place of defense: Universidad Politécnica de Lleida.
Place of preparation: Escuela Politécnica.

Summary: In the study of Markov chains classification of states is one of lascaracterísticas most important because it will depend on other properties comoson eg convergence of succession formed by the powers n-ésimas dela transition matrix associate and So asymptotic behavior. This problem has been addressed from the field of computing naturally through dosalgoritmos biological based on DNA and by the design of two P systems. Ambasmetodologías Computer naturally are uncertain although while DNA seobtienen results random appraisals, with the P systems obtienencálculos accurate. By contrast, the advantage presenting algorithms basadosen DNA is that today can already be implemented though perfeccionarde a substantial laboratory techniques. Finally note that lacomputación naturally opens the door to an exciting new model of computing that requires a change in thinking.

Author: ABADA GARETA ALBERTO.
Year: 2006.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: AULA MERIT-010 EDIFICI D5 - CAMPUS NORD.
Place of preparation: DA 205 NORD.