No description available.

No description available.

No description available.

Estudamos a teoria de processos de ramicação de Galton-Watson a tempo discreto e as ferramentas probabilísticas necessárias para analisa-los. Na primeira etapa, demos um tratamento básico de processos de ramicação, isto e, assumimos que as partículas são iguais e que a distribuição do número de descendentes diretos de cada partícula e sempre a mesma. Também incluímos resultados sobre o comportamento limite para os casos subcrítico, crítico e supercrítico. Posteriormente, consideramos uma generalização das características assumidas na etapa anterior, baseada em processos de Galton-Watson em meios variáveis, onde a distribuição do número de descendentes diretos de uma partícula varia de geração em geração. Estudamos e provamos teoremas limite. Finalmente, discutimos dois modelos de processos de ramificação binária com aplicações em biologia. / We study the theory of Galton-Watson branching processes at discrete time and the necessary probabilistic tools to analyze them. In the first stage, was given a basic treatment of the branching processes, that is, it was assumed that all the particles are equal and that the distribution of the number of offspring produced by a particle is always the same. Also were included some results about the asymptotic behavior for the subcritical, critical and supercritical cases. Afterwards, was considered a generalization of the characteristics assumed in the previous stage, based on Galton-Watson processes in varying environments, where the distribution of offspring produced by a particle varies from generation to generation. Were studied and proved limit theorems. Finally, were discussed two models of binary branching processes with applications in biology.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy February 1976 / This thesis treats systems of ordinary differential equations that ar*? extracted from ch-_ Kolmogorov forward equations of a class of Markov processes, known generally as birth and death processes. In particular we extract and analyze systems of equations which describe the dynamic behaviour of the second-order moments of the probability distribution of population governed by birth and death processes. We show that these systems form an important class of stochastic population models and conclude that they are superior to those stochastic models derived by adding a noise term to a deterministic population model. We also show that these systems are readily used in population control studies, in which the cost of uncertainty in the population mean size is taken into account. The first chapter formulates the univariate linear birth and death process in its most general form. T i«- prvbo'. i: ity distribution for the constant parameter case is obtained exactly, which allows one to state, as special cases, results on the simple birth and death, Poisson, Pascal, Polya, Palm and Arley processes. Control of a popu= lation, modelled by the linear birth and death process, is considered next. Particular attention is paid to system performance indecee which take into account the cost associated with non-zero variance and the cost of improving initial estimates of the size of the popula” tion under control.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2014 / Matrix models, and their associated integrals, are encoded with a rich structure, especially when studied in the large N limit. In our project we study the dynamics of a Gaussian ensemble of m complex matrices or 2m hermitian matrices for d = 0 and d = 1 systems. We rst investigate the two hermitian matrix model parameterized in \matrix valued polar coordinates", and study the integral and the quantum mechanics of this system. In the Hamiltonian picture, the full Laplacian is derived, and in the process, the radial part of the Jacobian is identi ed. Loop variables which depend only on the eigenvalues of the radial matrix turn out to form a closed subsector of the theory. Using collective eld theory methods and a density description, this Jacobian is independently veri ed. For potentials that depend only on the eigenvalues of the radial matrix, the system is shown to be equivalent to a system of non-interacting (2+1)-dimensional \radial fermions" in a harmonic potential. The matrix integral of the single complex matrix system, (d = 0 system), is studied in the large N semi-classical approximation. The solutions of the stationary condition are investigated on the complex plane, and the eigenvalue density function is obtained for both the single and symmetrically extended intervals of the complex plane. The single complex matrix model is then generalized to a Gaussian ensemble of m complex matrices or 2m hermitian matrices. Similarly, for this generalized ensemble of matrices, we study both the integral of the system and the Hamiltonian of the system. A closed sector of the system is again identi ed consisting of loop variables that only depend on the eigenvalues of a matrix that has a natural interpretation as that of a radial matrix. This closed subsector possess an enhanced U(N)m+1 symmetry. Using the Schwinger-Dyson equations which close on this radial sector we derive the Jacobian of the change of variables to this radial sector. The integral of the system of m complex matrices is evaluated in the large N semi-classical approximation in a density description, where we observe the emergence of a new logarithmic term when m 2. The solutions of the stationary condition of the system are investigated on the complex plane, and the eigenvalue density functions for m 2 are obtained in the large N limit. The \fermionic description" of the Gaussian ensemble of m complex matrices in radially invariant potentials is developed resulting in a sum of non-interacting Hamiltonians in (2m + 1)-dimensions with an induced singular term, that acts on radially anti-symmetric wavefunctions. In the last chapter of our work, the Hamiltonian of the system of m complex matrices is formulated in the collective eld theory formalism. In this density description we will study the large N background and obtain the eigenvalue density function.

No description available.

by Lau Chung Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1980. / Bibliography: leaf 90.

by Yuk-ka Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 73-74). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Regenerative Simulation --- p.5 / Chapter § 2.1 --- Discrete time discrete state space Markov chain --- p.5 / Chapter § 2.2 --- Discrete time continuous state space Markov chain --- p.8 / Chapter Chapter 3 --- Estimation --- p.14 / Chapter § 3.1 --- Ratio estimators --- p.14 / Chapter § 3.2 --- General method for generation of steady states from the estimated stationary distribution --- p.17 / Chapter § 3.3 --- Bootstrap method --- p.22 / Chapter § 3.4 --- A new approach: the scoring method --- p.26 / Chapter § 3.4.1 --- G(0) method --- p.29 / Chapter § 3.4.2 --- G(1) method --- p.31 / Chapter Chapter 4 --- Bias of the Scoring Sampling Algorithm --- p.34 / Chapter § 4.1 --- General form --- p.34 / Chapter § 4.2 --- Bias of G(0) estimator --- p.36 / Chapter § 4.3 --- Bias of G(l) estimator --- p.43 / Chapter § 4.4 --- Estimation of bounds for bias: stopping criterion for simulation --- p.51 / Chapter Chapter 5 --- Simulation Study --- p.54 / Chapter Chapter 6 --- Discussion --- p.70 / References --- p.73

So-Kuen Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 99-102). / Chapter Chapter One --- Preview --- p.1 / Chapter Section 1 --- Introduction --- p.1 / Chapter Section 2 --- The Life Time Distribution --- p.4 / Chapter 2.1 --- Exponential Distribution --- p.5 / Chapter 2.2 --- Gamma Distribution --- p.6 / Chapter 2.3 --- Weibull Distribution --- p.7 / Chapter 2.4 --- Lognormal Distribution --- p.10 / Chapter Section 3 --- Nonparametric Inference for Geometric Process --- p.13 / Chapter 3.1 --- Test for Geometric Process --- p.13 / Chapter 3.2 --- Nonparametric Estimation Method --- p.17 / Chapter Section 4 --- Test for Distribution --- p.20 / Chapter 4.1 --- Graphical Method --- p.20 / Chapter 4.2 --- KS-test --- p.22 / Chapter 4.3 --- x2 GOF-test --- p.27 / Chapter 4.4 --- F-test (Exponential Dist.) --- p.28 / Chapter Chapter Two --- Parametric Inference for Geometric Process --- p.29 / Chapter Chapter Three --- Simulations --- p.39 / Chapter Chapter Four --- Examples --- p.49 / Chapter Chapter Five --- Comparison and Conclusion --- p.57 / Tables and Graphs --- p.61 / References --- p.99