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This book explains the basic theory of Hilbert C*-module in detail, covering a wide range of applications from generalized index to module framework. At the center of the book, the Beurling-Deny criterion is characterized between operator valued Dirichlet forms and quantum Markov semigroups, hence opening a new field of quantum probability research. The general scope of the book includes: basic theory of Hilbert C*-modules; generalized indices and module frames; operator valued Dirichlet forms; and quantum Markov semigroups. This book will be of value to scholars and graduate students in the fields of operator algebra, quantum probability and quantum information.

Operator theory. --- Functional analysis. --- Markov processes. --- Operator Theory. --- Functional Analysis. --- Markov Process. --- Hilbert modules.

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This paper addresses several shortcomings in the productivity and markup estimation literature. Using Monte-Carlo simulations, the analysis shows that the methods in Ackerberg, Caves and Frazer (2015) and De Loecker and Warzynski (2012) produce biased estimates of the impact of policy variables on markups and productivity. This bias stems from endogeneity due to the following: (1) the functional form of the production function; (2) the omission of demand shifters; (3) the absence of price information; (4) the violation of the Markov process for productivity; and (5) misspecification when marginal costs are excluded in the estimation. The paper addresses these concerns using a quasi-maximum likelihood approach and a generalized estimator for the production function. It produces unbiased estimates of the impact of regulation on markups and productivity. The paper therefore proposes a work-around solution for the identification problem identified in Bond, Hashemi, Kaplan and Zoch (2020), and an unbiased measure of productivity, by directly accounting for the joint impact of regulation on markups and productivity.

Competition Policy --- Enterprise Development and Reform --- Legal Regulation and Business Environment --- Markov Process --- Markups --- Private Sector Development --- Production Function --- Productivity --- Quasi-Maximum Likelihood --- Regulation

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Ecology --- -Balance of nature --- Biology --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Mathematics --- Biomathematics. Biometry. Biostatistics --- General ecology and biosociology --- Mathematics. --- ecology --- Statistical methods --- Data processing --- data collection --- mathematics --- Balance of nature --- Environmental sciences --- Population biology --- MARKOV PROCESS --- Structure analysis --- Cluster analysis --- ECOLOGY --- Leslie matrix --- Monograph --- Ecology. --- Correlation (Statistics) --- Multivariate analysis --- Spatial analysis (Statistics) --- Ecology - Mathematics --- Ecologie --- Ecologie mathematique --- Modelisation mathematique --- Mathematiques

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This book provides a compact introduction to the theory of measure-valued branching processes, immigration processes and Ornstein–Uhlenbeck type processes. Measure-valued branching processes arise as high density limits of branching particle systems. The first part of the book gives an analytic construction of a special class of such processes, the Dawson–Watanabe superprocesses, which includes the finite-dimensional continuous-state branching process as an example. Under natural assumptions, it is shown that the superprocesses have Borel right realizations. Transformations are then used to derive the existence and regularity of several different forms of the superprocesses. This technique simplifies the constructions and gives useful new perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The second part investigates immigration structures associated with the measure-valued branching processes. The structures are formulated by skew convolution semigroups, which are characterized in terms of infinitely divisible probability entrance laws. A theory of stochastic equations for one-dimensional continuous-state branching processes with or without immigration is developed, which plays a key role in the construction of measure flows of those processes. The third part of the book studies a class of Ornstein-Uhlenbeck type processes in Hilbert spaces defined by generalized Mehler semigroups, which arise naturally in fluctuation limit theorems of the immigration superprocesses. This volume is aimed at researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.

Probabilities. --- Stochastic processes. --- Markov processes. --- Probability Theory. --- Stochastic Processes. --- Markov Process. --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Random processes --- Probabilities --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Processos de ramificació --- Processos de Markov --- Processos estocàstics --- Moviment brownià --- Processos de difusió --- Processos de moviment brownià --- Cladística --- Branching processes. --- Processes, Branching

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The volume includes a collection of peer-reviewed contributions from among those presented at the main conference organized yearly by the Mexican Statistical Association (AME) and every two years by a Latin-American Confederation of Statistical Societies. For the 2018 edition, particular attention was placed on the analysis of highly complex or large data sets, which have come to be known as “big data”. Statistical research in Latin America is prolific and research networks span within and outside the region. The goal of this volume is to provide access to selected works from Latin-American collaborators and their research networks to a wider audience. New methodological advances, motivated in part by the challenges of a data-driven world and the Latin American context, will be of interest to academics and practitioners around the world. .

Markov processes. --- Statistics . --- Big data. --- Markov model. --- Applied Statistics. --- Bayesian Inference. --- Big Data/Analytics. --- Big Data. --- Data sets, Large --- Large data sets --- Data sets --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Mathematical statistics --- Mathematical statistics. --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistics. --- Quantitative research. --- Markov Process. --- Data Analysis and Big Data. --- Data analysis (Quantitative research) --- Exploratory data analysis (Quantitative research) --- Quantitative analysis (Research) --- Quantitative methods (Research) --- Research