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This unique volume discusses some recent developments in the theory of spatial branching processes and superprocesses, with special emphasis on spines, laws of large lumbers, interactions and random media. Although this book is mainly written for mathematicians, the models discussed are relevant to certain models in population biology, and are thus hopefully interesting to the applied mathematician/biologist as well. The necessary background material in probability and analysis is provided in a comprehensive introductory chapter. Historical notes and several exercises are provided to complement each chapter.

Mathematical statistics. --- Branching processes. --- Law of large numbers. --- Large numbers, Law of --- Numbers, Large --- Convergence --- Mathematical statistics --- Probabilities --- Processes, Branching --- Stochastic processes --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistical methods

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This book offers a comprehensive guide to large sample techniques in statistics. More importantly, it focuses on thinking skills rather than just what formulae to use; it provides motivations, and intuition, rather than detailed proofs; it begins with very simple techniques, and connects theory and applications in entertaining ways. The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first 10 chapters contains at least one section of case study. The last five chapters are devoted to special areas of applications. The sections of case studies and chapters of applications fully demonstrate how to use methods developed from large sample theory in various, less-than-textbook situations. The book is supplemented by a large number of exercises, giving the readers plenty of opportunities to practice what they have learned. The book is mostly self-contained with the appendices providing some backgrounds for matrix algebra and mathematical statistics. The book is intended for a wide audience, ranging from senior undergraduate students to researchers with Ph.D. degrees. A first course in mathematical statistics and a course in calculus are prerequisites. Jiming Jiang is a Professor of Statistics at the University of California, Davis. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. He is the author of another Springer book, Linear and Generalized Linear Mixed Models and Their Applications (2007). Jiming Jiang is a prominent researcher in the fields of mixed effects models, small area estimation and model selection. Most of his research papers have involved large sample techniques. He is currently an Associate Editor of the Annals of Statistics.

Electronic books. -- local. --- Statistics -- Data processing. --- Sampling (Statistics) --- Law of large numbers --- Mathematical statistics --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Statistics --- Data processing. --- Mathematics. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk --- Math --- Science --- Distribution (Probability theory. --- Mathematical statistics. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistics, Mathematical --- Law of large numbers. --- Statistics .

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Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation. Using the tools of optimization over vector spaces, Egerstedt and Martin demonstrate how all of these problems are part of the same general mathematical framework, and how they are all, to a certain degree, a consequence of the optimization problem of finding the shortest distance from a point to an affine subspace in a Hilbert space. They cover periodic splines, monotone splines, and splines with inequality constraints, and explain how any finite number of linear constraints can be added. This book reveals how the many natural connections between control theory, numerical analysis, and statistics can be used to generate powerful mathematical and analytical tools. This book is an excellent resource for students and professionals in control theory, robotics, engineering, computer graphics, econometrics, and any area that requires the construction of curves based on sets of raw data.

Interpolation. --- Smoothing (Numerical analysis) --- Smoothing (Statistics) --- Curve fitting. --- Splines. --- Spline theory. --- Spline functions --- Approximation theory --- Interpolation --- Joints (Engineering) --- Mechanical movements --- Harmonic drives --- Fitting, Curve --- Numerical analysis --- Least squares --- Statistics --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Graphic methods --- Accuracy and precision. --- Affine space. --- Affine variety. --- Algorithm. --- Approximation. --- Arbitrarily large. --- B-spline. --- Banach space. --- Bernstein polynomial. --- Bifurcation theory. --- Big O notation. --- Birkhoff interpolation. --- Boundary value problem. --- Bézier curve. --- Chaos theory. --- Computation. --- Computational problem. --- Condition number. --- Constrained optimization. --- Continuous function (set theory). --- Continuous function. --- Control function (econometrics). --- Control theory. --- Controllability. --- Convex optimization. --- Convolution. --- Cubic Hermite spline. --- Data set. --- Derivative. --- Differentiable function. --- Differential equation. --- Dimension (vector space). --- Directional derivative. --- Discrete mathematics. --- Dynamic programming. --- Equation. --- Estimation. --- Filtering problem (stochastic processes). --- Gaussian quadrature. --- Gradient descent. --- Gramian matrix. --- Growth curve (statistics). --- Hermite interpolation. --- Hermite polynomials. --- Hilbert projection theorem. --- Hilbert space. --- Initial condition. --- Initial value problem. --- Integral equation. --- Iterative method. --- Karush–Kuhn–Tucker conditions. --- Kernel method. --- Lagrange polynomial. --- Law of large numbers. --- Least squares. --- Linear algebra. --- Linear combination. --- Linear filter. --- Linear map. --- Mathematical optimization. --- Mathematics. --- Maxima and minima. --- Monotonic function. --- Nonlinear programming. --- Nonlinear system. --- Normal distribution. --- Numerical analysis. --- Numerical stability. --- Optimal control. --- Optimization problem. --- Ordinary differential equation. --- Orthogonal polynomials. --- Parameter. --- Piecewise. --- Pointwise. --- Polynomial interpolation. --- Polynomial. --- Probability distribution. --- Quadratic programming. --- Random variable. --- Rate of convergence. --- Ratio test. --- Riccati equation. --- Simpson's rule. --- Simultaneous equations. --- Smoothing spline. --- Smoothing. --- Smoothness. --- Special case. --- Spline (mathematics). --- Spline interpolation. --- Statistic. --- Stochastic calculus. --- Stochastic. --- Telemetry. --- Theorem. --- Trapezoidal rule. --- Waypoint. --- Weight function. --- Without loss of generality.

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The aim of this Special Issue of Mathematics is to commemorate the outstanding Russian mathematician Vladimir Zolotarev, whose 90th birthday will be celebrated on February 27th, 2021. The present Special Issue contains a collection of new papers by participants in sessions of the International Seminar on Stability Problems for Stochastic Models founded by Zolotarev. Along with research in probability distributions theory, limit theorems of probability theory, stochastic processes, mathematical statistics, and queuing theory, this collection contains papers dealing with applications of stochastic models in modeling of pension schemes, modeling of extreme precipitation, construction of statistical indicators of scientific publication importance, and other fields.

continuous-time Markov chains --- non-stationary Markovian queueing model --- stability --- perturbation bounds --- forward Kolmogorov system --- threshold processing --- random samples --- long-term dependence --- mean-square risk estimate --- integrals and sums --- rates of convergence --- conditional law of large numbers --- conditional central limit theorem --- stochastic differential observation system --- nonlinear filtering problem --- state-dependent observation noise --- numerical filtering algorithm --- filtering given time-discretized observations --- stable approximation --- approximation accuracy --- Rényi theorem --- Kantorovich distance --- zeta-metrics --- Stein’s method --- stationary renewal distribution --- equilibrium transform --- geometric random sum --- characteristic function --- precipitation --- limit theorems --- statistical test --- generalized negative binomial distribution --- generalized gamma distribution --- asymptotic approximations --- extreme order statistics --- random sample size --- slowly varying --- monotony in the Zygmund sense --- class Γa(g) --- self-neglecting function --- convergence rates --- citation distribution --- Hirsch index --- geometric distribution --- Sibuya distribution --- geometrically stable distribution --- generalized Linnik distribution --- random sum --- transfer theorem --- multivariate normal scale mixtures --- heavy-tailed distributions --- multivariate stable distribution --- multivariate Linnik distribution --- generalized Mittag–Leffler distribution --- multivariate generalized Mittag–Leffler distribution --- stable distribution --- probability density function --- distribution function --- Hankel contours --- multivariate stable processes --- contour integrals --- fractional laplacian --- second order expansions --- high-dimensional --- low sample size --- Laplace distribution --- Student’s t-distribution --- pareto mixture distribution --- multiserver system --- uniform distance --- perfect simulation --- priority system --- marked Markov arrival process --- phase-type distribution --- change of the priority --- dispatching --- heterogeneous servers --- Markov decision process --- policy-iteration algorithm --- mean number of customers --- decomposable semi-regenerative process --- multiple power series distribution --- integral limit theorem --- local limit theorem --- Tauberian lemma --- R-weakly one-sided oscillation of the multiple sequence at infinity along the given multiple sequence --- pension schemes --- balance equation --- gross premium --- premium load --- lump sum --- defined contribution pension schemes --- decrement tables --- robustness --- minimax approach --- stable estimation